Sums of periodic Darboux functions and measurability

by

T. Natkaniec, W. Wilczynski

7 pages; preprint.

We show that a function f:R-->R can be represented as a sum of n Darboux periodic functions if and only if it can be represented as a sum of n periodic functions. Also it is shown that even functions having very simple structure cannot be represented as a sum of n>1 Lebesgue'e measurable periodic functions.


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Last modified May 17, 2002.