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There exists in truth a 1-toone correspondence amongst the set functions around the 1 hand, and The purpose functions on one other. both of those details of watch are helpful check here in probability theory. We establish initially the easier 50 percent of this correspondence. Lemma. (4)
This getting accurate for e extremely preference in the A j' s, the file (X )' s are independent by definition. The proof of another theorem is comparable and is left as an training.
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the second equation currently being a subject of easy algebra. Now let Xj be an r.v. (specifically an arbitrary operate) on Q j ; B j be an arbitrary Borel set; and S j = Xj I (B j), particularly:
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1. for almost any countably infinite established Q, the gathering of its finite subsets and their complements kinds a field ?ft. If we determine ~(E) on q; being 0 or 1 according as E is finite or not, then qp is finitely additive but not countably so.
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