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Category analogue of sup-measurability problem

Ciesielski K., Shelah S.

Journal of Applied Analysis

2000

Vol. 6, nr 2

159-172

A function F: R2→ R is called sup-measurable if Ff : R→ R given by Ff(x) = F(x,f(x)), x ∈R, is measurable for each measurable function f: R→ R. It is known that under different set theoretical assumptions, including CH, there are sup-measurable non-measurable functions, as well as their category analogues. In this paper we will show that the existence of the category analogues of sup-measurable non-measurable functions is independent of ZFC. A similar result for the original measurable case is the subject of a work in prepartion by Rosłanowski and Shelah.

On the Peano derivaties of functions having the Baire property

Hejduk J.

Demonstratio Mathematica

1998

Vol. 31, nr 3

663-668

We present the result that the set of points, where the I-approximate Peano derivatives of function having the Baire property exists, has the Baire property.