Research Article

A strong law of large numbers for non identically distributed Pettis integrable random sets in a general Banach space

Published in: Quaestiones Mathematicae
Volume 46 , issue 7 , 2023 , pages: 1347–1366

DOI: 10.2989/16073606.2022.2074324

Author(s): M. El Allali University Sidi Mohamed Ben Abdellah, FSTF, Morocco , F. Ezzaki University Sidi Mohamed Ben Abdellah, FSTF, Morocco

Keywords: 60B12 , 60E05 , 60F15 , 60G50 , Pettis integration , strong law of large numbers , random sets , Cesàro mean convergence theorem

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Abstract

A multivalued version of Cesàro mean convergence theorem is established. As a consequence, various convergence results of strong law of large numbers for pairwise independent Pettis integrable random sets in a Banach space without any additional geometric condition on the space are provided.

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