geometry of banach space
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Birkhoff-James Orthogonality and Its Application in the Study of Geometry of Banach Space

Advanced Topics in Mathematical Analysis ◽

10.1201/9781351142120-8 ◽

2019 ◽

pp. 245-284

Author(s):

Kallol Paul ◽

Debmalya Sain

Keyword(s):

Banach Space ◽

Geometry Of Banach Space ◽

James Orthogonality

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Strong Laws of Large Numbers for𝔹-Valued Random Fields

Discrete Dynamics in Nature and Society ◽

10.1155/2009/485412 ◽

2009 ◽

Vol 2009 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Zbigniew A. Lagodowski

Keyword(s):

Banach Space ◽

Random Fields ◽

Law Of Large Numbers ◽

Random Vectors ◽

Strong Law ◽

Laws Of Large Numbers ◽

Strong Laws ◽

Large Numbers ◽

Geometry Of Banach Space ◽

Necessary And Sufficient

We extend to random fields case, the results of Woyczynski, who proved Brunk's type strong law of large numbers (SLLNs) for𝔹-valued random vectors under geometric assumptions. Also, we give probabilistic requirements for above-mentioned SLLN, related to results obtained by Acosta as well as necessary and sufficient probabilistic conditions for the geometry of Banach space associated to the strong and weak law of large numbers for multidimensionally indexed random vectors.