What's the proof of this fundamental theorem?(adsbygoogle = window.adsbygoogle || []).push({});

Let (X,B,u) and (Y,C,v) be sigma finite measure spaces, Let f in L1(X,B,u) and g in L1(Y,C,v). Let h(x,y)=f(x)g(y).

Then, h is in L1(XxY,BxC,uxv) and

[tex]\int hd(u\times v)=\int fdu \int gdv[/tex]

should be an easy application of fubini,but i really have no idea to how work it out

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# Product measure

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