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 n...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-convergence展开更多
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)
文摘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-convergence
