Abstract
Let M(X) be the ring of all real measurable functions on a measurable space
(X,A). In this article, we show that every ideal of M(X) is a Z?-ideal.
Also, we give several characterizations of maximal ideals of M(X), mostly in
terms of certain lattice-theoretic properties of A. The notion of
T-measurable space is introduced. Next, we show that for every measurable
space (X,A) there exists a T-measurable space (Y,A') such that M(X) ? M(Y)
as rings. The notion of compact measurable space is introduced. Next, we
prove that if (X,A) and (Y,A') are two compact T-measurable spaces, then X
? Y as measurable spaces if and only if M(X) ? M(Y) as rings.
Publisher
National Library of Serbia
Cited by
1 articles.
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