Abstract
In this note we present some results on typical properties of the chain recurrent sets of bounded Baire one functions. In particular we show that typical members of bounded Baire one functions have closed chain recurrent sets and μ(A(f))=0, where μ is an arbitrary finite Borel measure on the unit interval and A(f) is the closure of the set of chain recurrent points of f or any of its subsets.
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