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Stochastic Limit TheoryAn Introduction for Econometricians$
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James Davidson

Print publication date: 1994

Print ISBN-13: 9780198774037

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774036.001.0001

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(p.143) 10 Conditioning
Stochastic Limit Theory

James Davidson

Oxford University Press

This chapter deals in depth with the concept of conditional expectation. This is defined first in the traditional “naïve” manner, and then using the measure theoretic approach. A comprehensive set of properties of the conditional expectation are proved, generalizing several results of Ch. 9, and then multiple sub‐σ‐fields and nesting are considered, and a brief treatment of conditional distributions and conditional independence.

Keywords:   conditional distributions, conditional expectation, conditional independence, conditional inequalities, iterated expectations, nested sub‐σ‐fields, regular conditioning

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