- Doob–Dynkin lemma
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In mathematics, the Doob–Dynkin lemma, named after Joseph Doob and Eugene Dynkin, is a statement in probability theory that characterizes the situation when one random variable is a function of another, in terms of measurability and σ algebras.
Statement of the lemma
Let
and σ(X) be the σ algebra generated by X. Then Y is σ(X) measurable if and only if Y = g(X) for some Borel measurable function
.
References
- A. Bobrowski: Functional analysis for probability and stochastic processes: an introduction, Cambridge University Press (2005), ISBN 0-521-83166-0
- M. M. Rao, R. J. Swift : Probability Theory with Applications, Mathematics and Its Applications, Band 582, Springer-Verlag (2006), ISBN 0-387-27730-7
See also
Categories:- Probability theorems
- Measure theory
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