Let (N, F, P) be a probability space. Let A = (An)nɛN be a countable partition of N, and let G = o(A). Let X be a real and integrable random variable. Show that E[X|G] = £E[X|A„] 1Am• nƐN

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Let (N, F,P) be a probability space. Let A = (An)nƐN be a countable partition
of N, and let G = o(A). Let X be a real and integrable random variable. Show
that
E[X|G] = _E[X| A„] 1An•
nƐN
Transcribed Image Text:Let (N, F,P) be a probability space. Let A = (An)nƐN be a countable partition of N, and let G = o(A). Let X be a real and integrable random variable. Show that E[X|G] = _E[X| A„] 1An• nƐN
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