Foundations of Modern Probability

Kallenberg, O. (2002). Foundations of Modern Probability. Springer.

Type

Book

Intellectual base

Review or monograph

Year

2002

DOI

10.1007/978-1-4757-4015-8

ISBN

9781441929495

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/978-1-4757-4015-8

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Doob–Dynkin lemma
  • The Doob–Dynkin lemma states, in its standard real-valued form, that f is measurable with respect to the sigma-algebra generated by T if and only if there is a measurable g on T's target such that \(f=g\circ T\); equivalent extensions require their target measurable-space hypotheses to be stated.

Mechanisms

• Measure-Space Specification
  • It is a declaration, not a proof: it asserts the measure and its scope so that every other mechanism has a fixed reference to check against.

    This sourceA measure space specifies a set, a sigma-algebra of measurable subsets, and a measure defined on that sigma-algebra.

Verification

Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.

Does it back the claim? Not recorded. Neither this nor any other of the 2 citations of this work carries a recorded support check.

Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.

See how references were verified.

Registry ID ref:69886f0a893b · see in the full table