A non-separable translation invariant extension of the Lebesgue measure space

DOI10.2307/1969434zbMath0040.20804OpenAlexW2335261899WikidataQ101311967 ScholiaQ101311967MaRDI QIDQ2648867

Shizuo Kakutani

Publication date: 1950

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1969434

Mathematics Subject Classification ID

Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (16)

On thick subgroups of uncountable \(\sigma \)-compact locally compact commutative groups ⋮ A large group of nonmeasurable additive functions ⋮ On uniform distribution for invariant extensions of the linear Lebesgue measure ⋮ Extensions of Haar measure for compact connected Abelian groups ⋮ Some remarks on the Steinhaus property for invariant extensions of the Lebesgue measure ⋮ Unnamed Item ⋮ Quasi-invariant measures on topological groups and \(\omega\)-powers ⋮ On ordinary and standard products of infinite family of \(\sigma \)-finite measures and some of their applications ⋮ Unnamed Item ⋮ Set-valued functions, Lebesgue extensions and saturated probability spaces ⋮ A nonseparable invariant extension of Lebesgue measure -- a generalized and abstract approach ⋮ On some methods of extending invariant and quasi-invariant measures ⋮ A combinatorial problem on translation-invariant extensions of the Lebesgue measure ⋮ Extensions of Haar measure and of harmonic analysis for locally compact Abelian groups ⋮ On sums of real-valued functions with extremely thick graphs ⋮ Extensions of Haar Measure to Relatively Large Nonmeasurable Subgroups

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