Unique Extension of Metric and Affine Connections to Finite Measures on Infinite Sample spaces
نویسنده
چکیده
It is known that there is a only one invariant metric, and only one family of invariant affine connections on the the space of probability measures on finite sample spaces. Under certain conditions this may also true for finite measures on finite sample spaces. We extends these results to finite measures on arbitrary sample spaces. It is shown that the generalization of these structures are unique. The metric is induced by the inner product on the Hilbert space of square root of measures, while the affine connection is induced by the affine structures of the Banach spaces of fractional powers of measues.
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