Transformations into Baire functions
Authors: A. M. Bruckner, Roy O. Davies and C. Goffman
Journal: Proc. Amer. Math. Soc. 67 (1977), 62-66
MSC: Primary 26A21
MathSciNet review: 0480903
Abstract: A measurable f from to R is equivalent to a Baire 2 function but may not be equivalent to any Baire 1 function. Gorman has obtained the following interesting contrasting facts. If f assumes finitely many values there is a homeomorphism h of I such that is equivalent to a Baire 1 function, but there is a measurable f which assumes countably many values which does not have this property. However, the example of Gorman is such that for some homeomorphisms h the function is not measurable. It is shown here that if is measurable, for every homeomorphism h, then there is an h for which is equivalent to a Baire 1 function.
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