Aleksandrov, A. B. Measurable partitions of a circumference generated by inner functions. (Russian. English summary) Zbl 0627.30033 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 149, 103-106 (1986). 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 Cited in 1 ReviewCited in 2 Documents MSC: 30D55 \(H^p\)-classes (MSC2000) 28A99 Classical measure theory Keywords:algebra; inner function; conditional expectation PDFBibTeX XMLCite \textit{A. B. Aleksandrov}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 149, 103--106 (1986; Zbl 0627.30033) Full Text: EuDML