Vitali type convergence theorems for Banach space valued integrals

DOI10.1007/s10114-013-2578-1zbMath1283.28003OpenAlexW2067506480MaRDI QIDQ381077

Marek Balcerzak, Kazimierz Musiał\

Publication date: 15 November 2013

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-013-2578-1

zbMATH Keywords

Pettis integral\(\mathcal I\)-convergenceconvergence theorems for integralsscalar convergence in measure

Mathematics Subject Classification ID

Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Convergence and divergence of series and sequences of functions (40A30) Vector-valued set functions, measures and integrals (28B05) Vector-valued measures and integration (46G10)

Related Items (8)

Nets and sequences of \(p\)-Bochner, \(p\)-Dunford and \(p\)-Pettis integrable functions with values in a Banach space ⋮ Convergence theorem of Pettis integrable multivalued pramart ⋮ A convergence theorem for the Birkhoff integral ⋮ On statistical convergence with respect to measure ⋮ Henstock-Kurzweil-Pettis integrability of compact valued multifunctions with values in an arbitrary Banach space ⋮ Unnamed Item ⋮ Nets and sequences of Riemann and Riemann-type integrable functions with values in a Banach space ⋮ Convergence for varying measures

Cites Work

• Statistical convergence and ideal convergence for sequences of functions
• Ideal version of Egorov's theorem for analytic P-ideals
• Statistical convergence in topology
• Generalized statistical convergence and convergence free spaces
• Pointwise \(\mathcal I\)-convergence and \(\mathcal I\)-convergence in measure of sequences of functions
• Weak and point-wise convergence in \(C(K)\) for filter convergence
• Pointwise limits of Birkhoff integrable functions
• Pettis integral and measure theory
• Analytic quotients: theory of liftings for quotients over analytic ideals on the integers
• Sur la convergence statistique
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