The Baire order of the functions continuous almost everywhere

Author:
R. Daniel Mauldin

Journal:
Proc. Amer. Math. Soc. **51** (1975), 371-377

MSC:
Primary 26A21

MathSciNet review:
0372128

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Abstract: Let be a complete and separable metric space and a -finite, complete Borel measure on with . Let be the family of all real-valued functions defined on whose set of points of discontinuity is of -measure 0. Let be the functions of Baire's class generated by . It is shown that if and only if is a purely atomic measure whose set of atoms forms a scattered subset of and that if , then the Baire order of is ; in other words, if , then . This answers a generalized version of a problem raised by Sierpinski and Felsztyn. An example is given of a normal space with Borel order 2 and Baire order .

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DOI:
https://doi.org/10.1090/S0002-9939-1975-0372128-1

Keywords:
Borel measure,
Baire's class ,
0-dimension,
scattered

Article copyright:
© Copyright 1975
American Mathematical Society