Professor Udayan B. Darji
University of Louisville, Louisville, Kentucky
Extensions Which Preserve Derivate Structures
In this talk we present two very general theorems from which a
classical theorem of Lusin and a classical theorem of Petruska
and Laczkovich follow readily. Our theorems are also very useful
for constructing pathological examples. For instance, as a simple
application of these theorems we can obtain continuous nowhere
monotone functions of bounded variation which have derivative
zero ae. We will also show how characterizations of certain
exceptional sets follow from these theorems as well.