Vitali Type Convergence Theorems for Banach Space Valued Integrals  

作　　者：Marek BALCERZAK Kazimierz MUSIAL 

机构地区：[1]Institute of Mathematics,Lodz University of Technology,ul.Wolczańska 215,93-005 Lodz,Poland [2]Institute of Mathematics,University of Wroclaw,Pl.Grunwaldzki 2/4,50-384 Wroclaw,Poland

出　　处：《Acta Mathematica Sinica,English Series》2013年第11期2027-2036,共10页数学学报（英文版）

基　　金：Supported by the Polish Ministry of Science and Higher Education(Grant Nos.N N201 414939 for M.Balcerzak,N N201 416139 for K.Musial)

摘　　要：Let （Ω,∑,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 Mso obtain a Vituli type Z-convergence theorem for Pettis integrals where Z is an ideal on N. Keywords Convergence theorems for integrals, Pettis integral, scalar equi-convergence in measure, Z-convergenceLet （Ω,∑,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 Mso obtain a Vituli type Z-convergence theorem for Pettis integrals where Z is an ideal on N. Keywords Convergence theorems for integrals, Pettis integral, scalar equi-convergence in measure, Z-convergence

关 键 词：Convergence theorems for integrals Pettis integral scalar equi-convergence in measure I-CONVERGENCE 28A20 28B05 40A10 40A30 46G10 

分 类 号：O177.2[理学—数学] O172.2[理学—基础数学]