Vitali type convergence theorems for Banach space valued integrals |
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| Authors: | Marek Balcerzak Kazimierz Musia? |
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| Institution: | [1]Institute of Mathematics, L6d2 University of Technology, ul. Wo1czanska 215, 93-005 Lodz, Poland [2]Institute of Mathematics, University of Wroclaw, Pl. Grunwaldzki 2/4, 50-384 Wroctaw, Poland |
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| Abstract: | Let (Ω, Σ, µ) be a complete probability space and let X be a Banach space. We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem. We also obtain a Vitali type I-convergence theorem for Pettis integrals where I is an ideal on ?. |
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| Keywords: | Convergence theorems for integrals Pettis integral scalar equi-convergence in measure I-convergence |
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