Pelc, Andrzej Combinatorics on \(\sigma\)-algebras and a problem of Banach. (English) Zbl 0599.28003 Fundam. Math. 123, 1-9 (1984). Certain problems related to a problem posed by Banach on measurable \(\sigma\)-algebras are addressed. For example, under certain set-theoretic assumptions (existence of a \(2^{\omega}\) scale, uniformity of Lebesgue measure), for any \(0<\kappa \leq \omega\), a collection of uniformly measurable \(\sigma\)-algebras is obtained such that any union of \(<\kappa\) of them generate a uniformly measurable \(\sigma\)-algebra and any union of \(\geq \kappa\) generate a nonmeasurable \(\sigma\)-algebra. Reviewer: J.W.Hagood MSC: 28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets 28A10 Real- or complex-valued set functions 03E15 Descriptive set theory 03E50 Continuum hypothesis and Martin’s axiom Keywords:countably generated measurable \(\sigma \) -algebras; Martin’s axiom; group-invariant version of Banach’s problem; scale PDFBibTeX XMLCite \textit{A. Pelc}, Fundam. Math. 123, 1--9 (1984; Zbl 0599.28003) Full Text: DOI EuDML