L-points of typical functions in the Zahorski classes (Q1088795)

The main result is the following: let \({\mathcal F}\) be any of the following subsets of the class of Baire 1 functions on [0,1]: \({\mathcal M}_ i\), b\({\mathcal M}_ i\), usc\({\mathcal M}_ i\), busc\({\mathcal M}_ i\), usc, busc where \(i=1,2,3,4\). Then \[ {\mathcal F}\cap \{x\in [0,1]:\lim_{h\to 0}\frac{1}{h}\int^{h}_{0}f(x+t)dt\quad does\quad not\quad exist\} \] is a closed, nowhere dense subset of \({\mathcal F}\).