Wikipedia:Reference desk/Archives/Mathematics/2008 March 15

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March 15[edit]

A measurable set?[edit]

Let and be measure spaces and sequences of sets of finite measure in X and Y respectively. Let the "rectangles" , and assume that

Let and

Why is it obvious that Tn is measurable?  — merge 17:01, 15 March 2008 (UTC)

Well, is just Bk if x is in Ak, and empty otherwise. So is the some of the measures of the Bk such that x is in Ak. Thus whether x is in Tn is determined by which of the Aks x is in, and Tn is a union of intersections of the Aks. Algebraist 17:45, 15 March 2008 (UTC)

Oh, I think I see how it works out. If is a sequence of nonnegative measurable real-valued functions and α is a real number, the sets

are measurable, and so are

and

.

In this case and .  — merge 22:30, 16 March 2008 (UTC)