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Conditional measures and operators |
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| Authors: | MM Rao |
| Institution: | University of California, Riverside, USA |
| Abstract: | A detailed study of the structure of conditional expectations and conditional probability measures is presented. Some characterizations of conditional expectations as a subclass of projection operators on Banach function spaces, and similarly conditional probabilities as a subclass of vector valued measures on such spaces are included. As applications of these results, a representation of Reynolds operators and related unified formulation of ergodic-martingale theorems are given. |
| Keywords: | 60B05 46G10 28A45 47A50 Conditional expectations conditional probability measures Jensen's inequality averaging and ?idák identities contractive projections regular and perfect conditional measures Dunford-Schwartz and order integrals Reynolds identity generalized martingale unified ergodic-martingale formulation disintegration of vector measures semivariation of conditional measures |
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