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Measurable partitions of a circumference generated by inner functions. (Russian. English summary) Zbl 0627.30033

Let \({\mathfrak M}\) be the Lebesgue \(\sigma\)-algebra of the unit circle \({\mathbb{T}}\). Every measurable function f on \({\mathbb{T}}\) generates the \(\sigma\)-algebra A(f), the least among all \(\sigma\)-algebras \(A\subset {\mathfrak M}\) containing all sets of zero length and such that f is measurable with respect to A. The article contains a criterion for a given \(\sigma\)-algebra \(A\subset {\mathfrak M}\) to be representable as A(f) for an inner function \(f\in H^{\infty}\). The criterion is the permutability of the Riesz projection with the operator of conditional expectation corresponding to A.
Reviewer: V.Khavin

MSC:

30D55 \(H^p\)-classes (MSC2000)
28A99 Classical measure theory
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