Theoretical analysis derives conditional expectation under non-finite measures without the Radon-Nikodym theorem, extending general probability theory.
The purpose of the present note is in part to extend results of Sidk [3] to cases where the measure is not finite, perhaps not even <r-finite. In particular, the conditional expectation of a random variable in Lx is obtained without the use of the Radon-Nikodym Theorem, which, indeed, does not apply with the required generality.
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H. D. Brunk (1963) studied this question.
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