Two dimensional probabilities with a given conditional structure

Josef Štěpán; Daniel Hlubinka

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The necessary and sufficient condition for a function $f : (0, 1) \to [0, 1]$ to be Borel measurable (given by Theorem stated below) provides a technique to prove (in Corollary 2) the existence of a Borel measurable map $H : {0, 1}^{ℕ} \to {0, 1}^{ℕ}$ such that $ℒ (H (X^{p})) = ℒ (X^{1 / 2})$ holds for each $p \in (0, 1)$ , where $X^{p} = (X_{1}^{p}, X_{2}^{p}, ...)$ denotes Bernoulli sequence of random variables with $P [X_{i}^{p} = 1] = p$ .

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Displaying similar documents to “Two dimensional probabilities with a given conditional structure”

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