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Conditional expectations for general measure spaces
- Source :
- Journal of Multivariate Analysis. 1:347-364
- Publication Year :
- 1971
- Publisher :
- Elsevier BV, 1971.
-
Abstract
- The classical conditional expectation with respect to σ-algebras, on probability measure spaces, has been extended for infinite measure spaces. In this paper we consider conditional expectations with respect to δ-rings, on arbitrary measure spaces. An additional condition has to be imposed in order to insure the uniqueness of the conditional expectation. The existence of the conditional expectation is proved for functions in Lp with 1 ≤ p < ∞, and, for localizable measures, also in L∞.The properties of the classical conditional expectation remain true in the general case, sometimes with some modifications.
- Subjects :
- Statistics and Probability
Discrete mathematics
Numerical Analysis
Pure mathematics
Conditional probability
Conditional probability distribution
δ-ring
Conditional expectation
Dynamic risk measure
Regular conditional probability
Standard probability space
Statistics, Probability and Uncertainty
infinite measure spaces
Conditional variance
Conditional expectations
Probability measure
Mathematics
Subjects
Details
- ISSN :
- 0047259X
- Volume :
- 1
- Database :
- OpenAIRE
- Journal :
- Journal of Multivariate Analysis
- Accession number :
- edsair.doi.dedup.....1fdfa8f3b06bd9c6340383464783b610