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ON THE STRONG LAW OF LARGE NUMBERS UNDER REARRANGEMENTS FOR SEQUENCES OF BLOCKWISE ORTHOGONAL RANDOM ELEMENTS IN BANACH SPACES
Author(s) -
Van Quang Nguyen,
Van Thanh Le
Publication year - 2007
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2007.00486.x
Subject(s) - mathematics , law of large numbers , banach space , type (biology) , space (punctuation) , random variable , pure mathematics , work (physics) , discrete mathematics , combinatorics , statistics , ecology , linguistics , philosophy , biology , mechanical engineering , engineering
Summary The condition of the strong law of large numbers is obtained for sequences of random elements in type p Banach spaces that are blockwise orthogonal. The current work extends a result of Chobanyan & Mandrekar (2000)[On Kolmogorov SLLN under rearrangements for orthogonal random variables in a B ‐space. J. Theoret. Probab. 13, 135–139.] Special cases of the main results are presented as corollaries, and illustrative examples are provided.