Abstract
A real-valued function f on R is called measurable if f−1(U) is measurable for every open set U in R. f is said to have the property of Baire if f−1 (U) has the property of Baire for every open set U in R. In either definition, U may be restricted to some base, or allowed to run over all Borel sets. The indicator function χ E of a set E ⊂ R is measurable if and only if E is measurable; χ E has the property of Baire if and only if E does.
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© 1980 Springer-Verlag New York Inc.
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Oxtoby, J.C. (1980). The Theorems of Lusin and Egoroff. In: Measure and Category. Graduate Texts in Mathematics, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9339-9_8
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DOI: https://doi.org/10.1007/978-1-4684-9339-9_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9341-2
Online ISBN: 978-1-4684-9339-9
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