Let (X,M,mu)be a measure space, E belongs to M, ME : {F belongs to M|F
subset of E}, muE := mu|ME, f : E to R ME measurable, fbar : X to Rbar
M measurable extension of f. prpve the following integral f dmuE
exists if and only if integral fbar chiE dmu exists, if so, bothe
integrals are equal.


  hint: fisrst assume that f is simple and then that f is nonnegative.

mu = lebesgue measure, M is measure.

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Clarification of Question by madukar-ga on 10 Dec 2002 18:53 PST

here ME means that script M where M is a measure and E is to the base M.

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Clarification of Question by madukar-ga on 11 Dec 2002 08:47 PST

he chi E is the characterstic function