A decomposition theorem for additive set-functions with applications to Pettis integrals and ergodic means

DOI10.1007/BF01214191zbMath0393.28005MaRDI QIDQ1252434

D. H. Fremlin, Michel Talagrand

Publication date: 1979

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/172865

zbMATH Keywords

Bounded Additive FunctionalBounded Scalarly Measurable FunctionContinuUm HypothesisDecompostion Theorem for Additive Set-FunctionsErgodic MeansHaar MeasureNatural Characteristic-Function MapNonmeasurable Cluster PointNontotally Bounded and Nonseparable RangesPerfect Probability SpacePettis IntegralPositive Additive FunctionalPurely Nonmeasurable

Mathematics Subject Classification ID

Real- or complex-valued set functions (28A10) Measure-preserving transformations (28D05) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Vector-valued set functions, measures and integrals (28B05) Set functions and measures on topological groups or semigroups, Haar measures, invariant measures (28C10) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Abstract differentiation theory, differentiation of set functions (28A15)

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