On the sets of fixed points of bounded Baire one functions

In this paper, we present some results on typical properties of the sets of fixed points of bounded Baire one functions. In particular, we show that typical elements of a uniformly closed subclass of such class of functions have nowhere dense set of fixed points. We also show that typical elements of the class of bounded Baire one functions have μ[f-1(F(f))] = 0, where μ is an arbitrary continuous Borel measure on the unit interval.