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Abstract
For a square integrable vector-valued process f on the Loeb product space, it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality. Various characterizations of almost sure uncorrelatedness for f are presented. The process f is also related to multilinear forms on the target Hilbert space. Finally, a general structure result for f involving the biorthogonal representation for the conditional expectation of f with respect to the usual product σ-algebra is presented.
Keywords
Keisler's pubini theorem, Loeb product space, Multilinear functional, Orthogonality, Uncorrelatedness, Vector-valued processes
Source Title
Transactions of the American Mathematical Society
Publisher
Series/Report No.
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Date
2004-08
DOI
10.1090/S0002-9947-03-03450-0
Type
Article