Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements  

作　　者：Robert PARKER Andrew ROSALSKY 

机构地区：[1]Department of Biostatistics, University of Florida [2]Department of Statistics, University of Florida

出　　处：《Acta Mathematica Sinica,English Series》2019年第5期583-596,共14页数学学报（英文版）

摘　　要：For a double array {V_(m,n), m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p(1 ≤ p ≤ 2) Banach space and an increasing double array {b_(m,n), m ≥1, n ≥ 1} of positive constants, the limit law ■ and in L_p as m∨n→∞ is shown to hold if ■ This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space.For a double array {V_(m,n), m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p(1 ≤ p ≤ 2) Banach space and an increasing double array {b_(m,n), m ≥1, n ≥ 1} of positive constants, the limit law ■ and in L_p as m∨n→∞ is shown to hold if ■ This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space.

关 键 词：Real separable BANACH SPACE DOUBLE array of independent random elements strong law of large numbers almost sure CONVERGENCE Rademacher type p BANACH SPACE CONVERGENCE in Lp 

分 类 号：O1[理学—数学]