A Note on Complete Convergence for Arrays of Rowwise Independent Banach Space Valued Random Elements

Abstract

We obtain complete convergence results for arrays of rowwise independent Banach space valued random elements. Compared with similar results presented in the probabilistic literature our conditions are weaker.

Keywords:

• Banach space valued random element
• Complete convergence
• Convergence in probability
• Rowwise independence

Mathematics Subject Classification:

• 60B12
• 60F15
• 60G50

The authors are grateful to the referee for carefully reading the manuscript and for providing some comments which helped them improve the presentation. The research of P. Chen was supported by the National Natural Science Foundation of China. The research of A. Volodin was partially supported by National Science and Engineering Research Council of Canada.