This article is cited in 2 papers

Short Communications

Strong Laws of Large Numbers for $B$-Valued $L_q$-Mixingale Sequences and the $q$-Smoothness of Banach Space

Gan Shixin

Department of Mathematics, Wuhan University

Abstract: In this paper a.s. convergence of Banach space valued $L_q$-mixingale sequences is proved. The result is used to establish a strong law of large numbers for Banach space valued $L_q$-mixingale sequences which has not been established previously. Conversely, $q$-smoothable Banach spaces are characterized in terms of strong laws of large numbers for these sequences.

Keywords: a.s. convergence, strong law of large numbers, Banach space valued $L_q$-mixingale sequences, smoothness of Banach space.

Received: 29.09.1998

Language: English

DOI: 10.4213/tvp3829

 English version: Theory of Probability and its Applications, 2002, 46:4, 717–721

Bibliographic databases:

• 
• 
•