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

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.

Mathematics Subject Classification (2020):

• 60B12
• 60E05
• 60F15
• 60G50

Key words:

• Pettis integration
• strong law of large numbers
• random sets
• Cesàro mean convergence theorem