Up: Set Theoretic Real Analysis
Previous: Elements of measure theory
References
- 1
- S. I. Adian, P. S. Novikov, On one semicontinuous
function, Uchen. Zap. MGPI W. I. Lenina 138 (1958), 3-10 (Russian);
Reprinted in: P. S. Novikov,
Collected papers. Set and function theory. Mathematical
Logic and algebra, ``Nauka,'' Moscow, 1979 (Russian).
- 2
- M. Balcerzak, Some remarks on sup-measurability, Real Anal.
Exchange 17 (1991-92), 597-607.
- 3
- M. Balcerzak, K. Ciesielski, T. Natkaniec,
Sierpinski-Zygmund functions that are
Darboux, almost continuous, or have a perfect road, Archive for Math. Logic,
to appear.
(Preprint available at
http://www.math.wvu.edu/homepages/kcies/)
- 4
- M. Balcerzak, D. Rogowska, Making some ideals meager on sets
of size of the continuum, Topology Proc., to appear.
- 5
- S. Baldwin, Martin's axiom implies a stronger version of
Blumberg's theorem, Real Anal. Exchange 16 (1990-91), 67-73.
- 6
- K. Banaszewski, T. Natkaniec, Sierpinski-Zygmund
functions that have the Cantor intermediate value property, preprint.
- 7
- T. Bartoszynski and H. Judah, Set Theory: on the structure of
the real line, A. K. Peters, 1995.
- 8
- A. Berarducci, D. Dikranjan, Uniformly approachable functions
and UA spaces, Rend. Ist. Matematico Univ. di Trieste 25 (1993), 23-56.
- 9
- H. Blumberg, New properties of all real functions, Trans.
AMS 24 (1922), 113-128.
- 10
- J. B. Brown, A
measure theoretic variant of Blumberg's theorem,
Proc. Amer. Math. Soc. 66 (1977), 266-268.
- 11
- J. B. Brown, Restriction theorems in real analysis,
Real Anal. Exchange 20(1) (1994-95), 510-526.
- 12
- J. B. Brown,
-Intersection Variant of Blumberg's Theorem,
preprint.
- 13
- J. B. Brown, P. Humke, and M. Laczkovich, Measurable Darboux
functions, Proc. Amer. Math. Soc. 102 (1988), 603-609.
- 14
- A. M. Bruckner, On characterizing classes of functions in terms
of associated sets, Canad. Math. Bull. 10 (1967), 227-231.
- 15
- A. M. Bruckner, Differentiation of real functions, CMR
Series vol. 5, American Math. Soc., 1994.
- 16
- A. M. Bruckner, The problem of characterizing derivatives
revisited, Real Anal. Exchange 21(1) (1995-96), 112-133.
- 17
- L. Bukovsky,
N. N. Kholshshevnikova, M. Repicky, Thin sets of harmonic analysis and
infinite combinatorics, Real Anal. Exchange 20(2) (1994-95), 454-509.
- 18
- M. R. Burke, K. Ciesielski, Sets on which measurable functions
are determined by their range, preprint.
(Available at
http://www.math.wvu.edu/homepages/kcies/)
- 19
- B. Cristian, I. Tevy, On characterizing connected functions,
Real Anal. Exchange 6 (1980-81), 203-207.
- 20
- J. Cichon, M. Morayne, Universal functions and
generalized classes of functions, Proc. Amer. Math. Soc. 102 (1988),
83-89.
- 21
- J. Cichon, M. Morayne, J. Pawlikowski, S. Solecki,
Decomposing Baire functions, J. Symbolic Logic 56(4) (1991), 1273-1283.
- 22
- K. Ciesielski, How good is the Lebesgue measure?,
Math. Intelligencer 11(2) (1989), 54-58.
- 23
- K. Ciesielski, Algebraically invariant extensions of
-finite measures on Euclidean spaces, Trans. Amer. Math. Soc.
318 (1990), 261-273.
- 24
- K. Ciesielski, Isometrically invariant extensions of
Lebesgue measure, Proc. Amer. Math. Soc.110 (1990), 799-801.
- 25
- K. Ciesielski, On range of uniformly antisymmetric
functions, Real Anal. Exchange 19 (1993-94), 616-619.
- 26
- K. Ciesielski, Topologizing different classes of real
functions, Can. J. Math. 46 (1994), 1188-1207.
- 27
- K. Ciesielski, Uniformly antisymmetric functions and
, Real Anal. Exchange 21 (1995-96), 147-153.
(Available at
http://www.math.wvu.edu/homepages/kcies/)
- 28
- K. Ciesielski, Sum and difference free partitions
of vector spaces, Colloq. Math. 71(2) (1996), 263-271.
(Available at
http://www.math.wvu.edu/homepages/kcies/)
- 29
- K. Ciesielski, Characterizing derivatives by preimages
of sets, preprint.
(Available at
http://www.math.wvu.edu/homepages/kcies/)
- 30
- K. Ciesielski, D. Dikranjan, S. Watson, Functions
characterized by images of sets, preprint.
(Available at
http://www.math.wvu.edu/homepages/kcies/)
- 31
- K. Ciesielski, K. Jasinski, Topologies making a given
ideal nowhere dense or meager, Topol. Appl. 63 (1995), 277-298.
- 32
- K. Ciesielski, L. Larson, Refinements of the density and
-density topologies, Proc. AMS 118 (1993), 547-553.
- 33
- K. Ciesielski, L. Larson, Uniformly antisymmetric functions,
Real Anal. Exchange 19 (1993-94), 226-235.
- 34
- K. Ciesielski, L. Larson, Sets of range uniqueness for
differentiable functions, in progress.
- 35
- K. Ciesielski, L. Larson, K. Ostaszewski, -density continuous functions, Memoirs of the Amer. Math. Soc., vol. 107
no. 515, 1994.
- 36
- K. Ciesielski, A. Maliszewski, Sums of bounded almost
continuous functions, Proc. Amer. Math. Soc., to appear. (Preprint
available at
http://www.math.wvu.edu/homepages/kcies/)
- 37
- K. Ciesielski, A. W. Miller, Cardinal invariants concerning
functions whose sum is almost continuous, Real Anal. Exchange 20
(1994-95), 657-672.
- 38
- K. Ciesielski, T. Natkaniec, Algebraic properties of the
class of Sierpinski-Zygmund functions, Topology Appl., to appear.
(Preprint
available at
http://www.math.wvu.edu/homepages/kcies/)
- 39
- K. Ciesielski, T. Natkaniec,
Darboux like functions that are characterizable by images,
preimages and associated sets, preprint. (Available at
http://www.math.wvu.edu/homepages/kcies/)
- 40
- K. Ciesielski, A. Pelc, Extensions of invariant
measures on Euclidean spaces, Fund. Math. 125 (1985), 1-10.
- 41
- K. Ciesielski, I. Rec aw, Cardinal invariants concerning
extendable and peripherally continuous functions, Real Anal. Exchange 21
(1995-96), 459-472. (Preprint
available at
http://www.math.wvu.edu/homepages/kcies/)
- 42
- K. Ciesielski, S. Shelah, Model with no magic set, in
progress.
- 43
- K. Ciesielski, M. Szyszkowski, A symmetrically continuous
function which is not countably continuous, Real Anal. Exchange 22
(1996-97), 428-432. (Preprint
available at
http://www.math.wvu.edu/homepages/kcies/)
- 44
- K. Ciesielski, J. Wojciechowski, Sums of connectivity
functions on , Proc. London Math. Soc., to appear.
(Preprint
available at
http://www.math.wvu.edu/homepages/kcies/)
- 45
- E. F. Collingwood, A. J. Lohwater,
The Theory of Cluster Sets, Cambridge University Press, Cambridge, 1966.
- 46
- P. Corazza, The generalized Borel conjecture and strongly
proper orders, Trans. Amer. Math. Soc. 316 (1989), 115-140.
- 47
- U. B. Darji, A Sierpinski-Zygmund function which has
a perfect road at each point, Colloq. Math. 64 (1993), 159-162.
- 48
- U. B. Darji, Some functions which are not countably
continuous, Invited talk the 19th Summer Symposium in Real Analysis, Real
Anal. Exchange 21(1) (1995-96), 19-25.
- 49
- U. B. Darji, P. D. Humke, Every bounded function is the sum of
three almost continuous bounded functions, Real Anal. Exchange 20
(1994-95), 367-369.
- 50
- R. O. Davies, Representation of functions of two variables
as sums of rectangular functions I, Fund. Math. 85 (1974), 177-183.
- 51
- R. Dougherty, M. Foreman, Banach-Tarski
decompositions using sets
with the property of Baire, J. Amer. Math. Soc. 7 (1994), 75-124.
- 52
- P. Erdos, On two problems of S. Marcus concerning
functions with the Darboux property, Rev. Roumaine Math. Pures et Appl. 9
(1964), 803-804.
- 53
- H. Fast, Une remarque sur la propriété de Weierstrass,
Coll. Math. 7 (1974), 125-128.
- 54
- C. Freiling, Axioms of Symmetry: throwing darts at the real
number line, J. Symb. Logic 51 (1986), 190-200.
- 55
- C. Freiling, A converse to a theorem of Sierpinski on
almost symmetric sets, Real Anal. Exchange 15 (1989-90), 760-767.
- 56
- C. Freiling, D. Rinne, A symmetric density property for
measurable sets, Real Anal. Exchange 14 (1988-89), 203-209.
- 57
- D. H. Fremlin, Cichon's diagram, Seminaire Initiation
a l'Analyse (eds. G. Choquet, M. Rogalski, J. Saint-Raymond), 23(5)
(1983-84).
- 58
- D. H. Fremlin, Real-valued-measurable cardinals, Israel
Mathematical Conference Proceedings, vol. 6 (1993), 151-304.
- 59
- D. H. Fremlin, Problems, circulated notes (1996).
- 60
- H. Friedman, A consistent Fubini-Tonelli theorem for
non-measurable functions, Illinois J. Math. 24 (1990), 390-395.
- 61
- R. G. Gibson, Darboux like functions, Abstract of the lecture
in Liptovsky Ján, September 1996, preprint.
- 62
- Z. Grande, J. Lipinski, Un exemple d'une fonction
sup-mesurable qui n'est pas mesurable, Colloq. Math. 39 (1978), 77-79.
- 63
- Z. Grande, A. Maliszewski, T. Natkaniec, Some problems
concerning almost continuous functions, Proceedings of the Joint US-Polish
Workshop in Real Analysis, Real Anal. Exchange 20 (1994-95), 429-432.
- 64
- W. Grudzinski, B. Koszela, T. Swiatkowski,
W. Wilczynski, Classes of continuous real functions (II), Real Anal.
Exchange 21 (1995-96), 407-423.
- 65
- M. Hagan, Equivalence of connectivity maps and
peripherally continuous transformations, Proc. Amer. Math. Soc. 17
(1966), 175-177.
- 66
- O. H. Hamilton, Fixed points for certain noncontinuous
transformations, Proc. Amer. Math. Soc. 8 (1957), 750-756.
- 67
- R. Hodel, Cardinal Functions I, in: Handbook of
Set-Theoretic Topology (eds. K. Kumem and J. E. Vaughan), North-Holland, 1984,
1-61.
- 68
- J. Jasinski, I. Rec aw,
Restrictions to Continuous and Pointwise Discontinuous Functions, preprint.
- 69
- F. Jordan, Cardinal invariants connected with adding
real functions, Real Anal. Exchange, to appear.
- 70
- F. Jordan, Private communication.
- 71
- I. Juhász, Cardinal functions in topology-ten years
later, Mathematisch Centrum, Amsterdam 1980.
- 72
- I. Juhász, Cardinal Functions II, in: Handbook of
Set-Theoretic Topology (eds. K. Kunen and J. E. Vaughan), North-Holland, 1984,
63-109.
- 73
- A. S. Kechris, A. Louveau, Descriptive Set Theory and the
Structure of Sets of Uniqueness, London Math. Soc. Lecture Note Ser. 128,
Cambridge, 1987.
- 74
- L. Keldys, Sur les fonctiones premières
mesurables B, Dokl. Akad. Nauk SSSR 4 (1934), 192-197.
- 75
- K. R. Kellum, Sums and limits of almost continuous functions,
Coll. Math. 31 (1974), 125-128.
- 76
- K. R. Kellum, Almost continuity and connectivity --
sometimes it's as easy to prove a stronger result, Real
Anal. Exchange 8 (1982-83), 244-252.
- 77
- A. B. Kharazishvili, On Sierpinski's problem concerning
strict extendability of an invariant measure, Soviet. Math. Dokl. 18
(1977), 71-74.
- 78
- A. B. Kharazishvili,
Invariant Extensions of
Lebesgue Measure, Izd. Tbilis. Univ., Tbilisi 1983. (in Russian)
- 79
- A. B. Kharazishvili, Applications of set theory, Tbilisi,
1989. (In russian.)
- 80
- B. Kirchheim, T. Natkaniec, On universally bad Darboux
functions, Real Anal. Exchange 16 (1990-91), 481-486.
- 81
- P. Komjáth, A note on Darboux functions, Real Anal.
Exchange 18 (1992-93), 249-252.
- 82
- P. Komjáth, Set theoretic constructions in Euclidean
spaces, in: New Trnds in Discrete and computational Geometry, (J. Pach, ed.)
Algorithms and Combinatorics 10 (1993), Springer-Verlag, 303-325.
- 83
- P. Komjáth, S. Shelah, On uniformly antisymmetric
functions, Real Anal. Exchange 19 (1993-94), 218-225.
- 84
- P. Komjáth, S. Shelah, Coloring finite subsets of
uncountable sets, Proc. Amer. Math. Soc., to appear.
- 85
- A. Krawczyk, P. Zakrzewski, Extensions of measures invariant
under countable groups of transformations, Trans. Amer. Math. Soc. 326
(1991), 211-226.
- 86
- K. Kunen, Set theory, North Holland, Amsterdam 1980.
- 87
- M. Laczkovich, Fubini's theorem and Sierpinski's set,
preprint, 1985.
- 88
- M. Laczkovich, unpublished preprint.
- 89
- M. Laczkovich, Equidecomposability and discrepancy; a
solution of Tarski's circle-squaring problem, J. reine und angew. Math
(Crelle's J.) 404 (1990), 77-117.
- 90
- M. Laczkovich, Paradoxical decompositions: a survey of
recent results, First European Congress of Mathematics, Vol II (Paris
1992), Birkhauser, Basel, 1994, 159-184.
- 91
- E. azarow, The coarsest topology for
-approximately continuous functions,
Comment. Math. Univ. Carolin. 27 (1986), 695-704.
- 92
- A. Lindenbaum, Sur quelques propriétés des fonctions de
variable réelle, Ann. Soc. Math. Polon. 6 (1927), 129-130.
- 93
- N. Luzin, Sur un problème de M. Baire, Hebdomadaires
Seances Acad. Sci. Paris 158 (1914), 1258-1261.
- 94
- A. Maliszewski, Sums of bounded Darboux functions, Real Anal.
Exchange 20 (1994-95), 673-680.
- 95
- P. Mahlo, Über Teilmengen des Kontinuums von dessen
Machtigkeit, Sitzungsberichte der Sachsischen Akademie der Wissenschaften
zu Leipzig, Mathematisch-Naturwissenschaftliche Klasse 65 (1913), 283-315.
- 96
- S. Marcus, Asupra unei teoreme de A. Lindenbaum si
demonstrate de W. Sierpinski, Acad. R. P. Romîne 19 (1960), 551-554.
- 97
-
I. Maximoff, Sur les fonctions ayant la propriété
de Darboux, Prace Mat.-Fiz. 43 (1936), 241-265.
- 98
- A. W. Miller, Some properties of measure and
category, Trans. Amer. Math. Soc. 266 (1981), 93-114.
- 99
- A. W. Miller, Mapping a set of reals onto the reals, J. Symb.
Logic 48 (1983), 575-584.
- 100
- A. W. Miller, Special Subsets of the Real
Line, in Handbook of Set-Theoretic Topology (K. Kunen and J.E. Vaughan, eds.),
North-Holland (1984), 201-233.
- 101
- A. W. Miller. Some interesting problems, circulated
notes, October 1996. Available at
http://www.math.wisc.edu/~miller.
- 102
- M. Morayne, On differentiability of Peano type
functions, Colloq. Math. 53 (1987), 129-132.
- 103
- S. Mrówka, Characterization of classes of functions
by Lebesgue sets, Czechoslovak Math. J. 19 (1969), 738-744.
- 104
- T. Natkaniec, Almost continuity, Real Anal. Exchange
17 (1991-1992), 462-520.
- 105
- T. Natkaniec, Almost continuity,
WSP Bydgoszcz 1992.
- 106
- T. Natkaniec, On a problem concerning
universally bad Darboux functions, Real
Anal. Exchange 18 (1992-1993), 471-475.
- 107
- T. Natkaniec, New cardinal invariants in real analysis,
Bull. Polish Acad. Sci. Math. 44 (1995), 251-256.
- 108
- T. Natkaniec, Extendability and almost continuity, Real
Anal. Exchange 21 (1995-1996), 349-355.
- 109
- T. Natkaniec, Some cardinal invariants in real
analysis, preprint.
- 110
- T. Natkaniec, I. Rec aw, Cardinal invariants concerning
functions whose product is almost continuous, Real Anal. Exchange 20
(1994-95), 281-285.
- 111
- J. C. Oxtoby, Measure and Category, 2nd ed., Springer-Verlag,
1980.
- 112
- W. Poreda, E. Wagner-Bojakowska,
The topology of -approximately continuous functions,
Rad. Mat. 2 (1986), 263-277.
- 113
- D. Preiss, M. Tartaglia, On characterizing derivatives, Proc.
Amer. Math. Soc. 123 (1995), 2417-2420.
- 114
- D. Rogowska, On a metric making a -ideal of subsets
of an uncountable Polish space meager, Tatra Mountains Math. Publ., in print.
- 115
- H. Rosen, On characterizing extendable connectivity functions
by associated sets, Real Anal. Exchange 22 (1996-97), 279-283.
- 116
- H. Rosen, R. G. Gibson, F. Roush, Extendable functions
and almost continuous functions with a perfect road, Real Anal. Exchange
17 (1991-92), 248-257.
- 117
- H. Sagan, A geometrization of Lebesgue's space-filling
curve, Math. Intelligencer 15(4) (1993), 37-43.
- 118
- S. Saks, Theory of the Integral, Warszawa-Lwów 1937.
- 119
- J. H. Schmerl, Countable partitions of Euclidean Space,
preprint.
- 120
- S. Shelah, Proper forcing, Springer-Verlag 1982.
- 121
- S. Shelah, Possibly every real function is continuous on a
non-meagre set, Publications de L'Institute Mathematique - Beograd, Nouvelle
Serie 57(71) (1995), 47-60.
- 122
- S. Shelah, J. Steprans, Decomposing Baire class 1
functions into continuous functions, Fund. Math. 145 (1994), 171-180.
- 123
- J. Shipman, Cardinal conditions for strong Fubini theorems,
Trans. Amer. Math. Soc. 321 (1990), 465-481.
- 124
- W. Sierpinski, Sur les rapports entre l'existence des
intégrales , et
, Fund. Math. 1 (1920), 142-147.
Reprinted in Oeuvres Choisies, vol. II, 341-345.
- 125
- W. Sierpinski, Sur un ensamble non dénombrable donte
toute image continue est de 1-er catégorie, Bull. Intern. Acad. Polon. Sci.
A 1928, 455-458. Reprinted in Oeuvres Choisies, vol. II, 671-674.
- 126
- W. Sierpinski, Sur un ensamble non dénombrable donte
toute image continue est de mesure null, Fund. Math. 11 (1928), 302-304.
Reprinted in Oeuvres Choisies, vol. II, 702-704.
- 127
- W. Sierpinski, Hypothèse du continu, Monografie
Matematyczne, Tom IV, Warsaw, 1934.
- 128
- W. Sierpinski, Sur une fonction non measurable partout
presque symetrique, Acta Litt. Scient (Szeged) 8 (1936),1-6. Reprinted
in Oeuvres Choisies, vol. III, 277-281.
- 129
- W. Sierpinski, Sur une propriété de fonctions
réelles quelconques définie dans les espaces métriques, Matematiche
(Catania) 8 (1953), no. 2, 73-78. Reprinted in Oeuvres Choisies, vol.
III, 665-668.
- 130
- W. Sierpinski, Oeuvres Choisies, Polish Scientific
Publishers PWN, Warsaw, 1974.
- 131
- W. Sierpinski, A. Zygmund, Sur une fonction qui est
discontinue sur tout ensemble de puissance du continu, Fund. Math. 4
(1923), 316-318. Reprinted in Oeuvres Choisies, vol. II, 497-499.
- 132
-
J. Stallings, Fixed point theorems for connectivity maps, Fund. Math.
47 (1959), 249-263.
- 133
- D. A. Sprecher
On functional complexity and superpositions of functions, Real
Anal. Exchange 9 (1983-1984), 417-431.
- 134
- J. Steprans, A very discontinuous Borel function,
J. Symbolic Logic 58 (1993), 1268-1283.
- 135
- J. Steprans, Sums of Darboux and continuous functions,
Fund. Math. 146 (1995), 107-120.
- 136
- J. Steprans, Decomposing with smooth sets, preprint.
- 137
- M. Tartaglia, Sulla caratterizzazione delle derivate, Pubbl.
Dip. Mat. Stat., Napoli, 1988.
- 138
- B. Thomson, Symmetric Properties of Real Functions, Marcel
Dekker, 1994.
- 139
- J. E. Vaughan, Small uncountable cardinals and topology, in:
Open Problems in Topology (eds. J. van Mill and G. M. Reed), North Holland,
1990, 197-218.
- 140
- D. J. Velleman, Characterizing Continuity, American Math.
Monthly, to appear.
- 141
- W. Wilczynski,
A generalization of the density topology,
Real Anal. Exchange 8 (1982-1983), 16-20.
- 142
- Z. Zahorski, Sur la première dérivée, Trans. Amer.
Math. Soc. 69 (1950), 1-54.
- 143
- P. Zakrzewski, Extensions of isometrically invariant measures
on Euclidean spaces, Proc. Amer. Math. Soc. 110 (1990), 325-331.
- 144
- P. Zakrzewski, Extending isomatrically invariant measures on
- a solution to Ciesielski's query, Real Anal. Exchange 21(2)
(1995-96), 582-589.