This reference and text offers a thorough analysis of conditional expectations
and probability measures, and demonstrates their important uses in real
situations. Coverage includes applications to sufficiency, Markov processes,
Martingales and analysis problems.;Presenting different characterizations of
conditional operators and meausures to illuminate the abstract and functional
analytic nature of conditioning, this volume: reviews the general concept of
conditioning; supplies Kolmogorov's formulation and its properties; provides an
axiomatic method for simplifying problems as an abstraction of Kolmogorov's
general formulation; explicates sufficient statistics; and illustrates
difficulties in the calculation of conditional expectations for continuous
multivariate distributions and provides methods for correct solutions in many
cases.;This work is designed as a reference for