Measurable Functions

  • Paul R. Halmos
Part of the Graduate Texts in Mathematics book series (GTM, volume 18)


A measurable space is a set X and a σ-ring S of subsets of X with the property that ⋃ S = X. Ordinarily it causes no confusion to denote a measurable space by the same symbol as the underlying set X; on the occasions when it is desirable to call attention to the particular σ-ring under consideration, we shall write (X,S) for X. It is customary to call a subset E of X measurable if and only if it belongs to the σ-ring S. This terminology is not meant to indicate that S is the σ-ring of all µ*-measurable sets with respect to some outer measure µ*, nor even that a non trivial measure is or may be defined on S.


Measurable Function Measure Space Uniform Convergence Simple Function Measure Zero 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media New York 1974

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  • Paul R. Halmos

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