On the sets of fixed points of bounded Baire one functions

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Abstract

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.

Original languageEnglish (US)
Article number1950040
JournalAsian-European Journal of Mathematics
Volume12
Issue number3
DOIs
StatePublished - Jun 1 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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