added fact from exercise sheet
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@ -146,3 +146,8 @@ for any $k \in \N$.
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\]
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hence $\bP[T] \in \{0,1\}$.
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\end{refproof}
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\begin{fact}+[Exercise 5.2 (b)]
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Any random variable measurable with respect to a $\bP$-trivial
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$\sigma$-algebra is a.s.~a constant.
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\end{fact}
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%\todo{copy proof}
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