Probability Measures on Separable Banach Spaces.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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The main purpose of this paper is to extend the definition of the covariance operator to the general set-up of a separable Banach space X, to obtain a direct relationship between the covariance operator and the natural isomorphism between the closure of X in L sub 2mu and the reproducing kernel Hilbert space, and to obtain some useful characterizations of a probability measure on X in terms of its covariance operator. The basic tool that is used to define the covariance operator is the Bochner integral.
- Statistics and Probability