Conditional measures and operators

M. M. Rao

Journal of Multivariate Analysis, 1975, vol. 5, issue 3, 330-413

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: Conditional; expectations; conditional; probability; measures; Jensens; inequality; averaging; and; Sidak; 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 (search for similar items in EconPapers)
Date: 1975
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