Real Analysis and Probability

Dudley, R. M. (2002). Real Analysis and Probability. Cambridge University Press.

Type

Book

Intellectual base

Review or monograph

Year

2002

DOI

10.1017/cbo9780511755347

ISBN

9780521809726

DOI registrant

Cambridge University Press

Link

https://doi.org/10.1017/cbo9780511755347

Cited by

3 citations across 3 artifacts.

Domain-specific

• Borel Set
  • It is not the same as a Lebesgue-measurable set: every Borel subset of \(\mathbb R\) is Lebesgue measurable, but the completed Lebesgue σ-algebra contains additional subsets of null sets.
• Doob–Dynkin lemma
  • … with respect to sigma(T), the lemma yields a Borel-measurable g with f equal to g(T). to A version of the conditional expectation of an integrable X given sigma(Y) can be expressed as h(Y) for a Borel-measurable h when Y and the version satisfy the applicable standard hypotheses. demonstrates that continuity.
• Lévy–Prokhorov metric
  • … transfers from Two point masses at locations distance delta apart have small Prokhorov distance because enlarging a set by delta captures the displaced mass. to A tightness proof shows a family is relatively compact by translating Prokhorov's theorem into compactness in the metric space of probability laws..

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