Measure Theory, Volume I

Vladimir I. Bogachev, M. T. (2007). Measure Theory, Volume I. Springer.

Type

Book

Intellectual base

Review or monograph

Year

2007

DOI

10.1007/978-3-540-34514-5

ISBN

9783540345138

Link

https://doi.org/10.1007/978-3-540-34514-5

Cited by

11 citations across 10 artifacts.

Domain-specific

• Borel measure
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Cylinder set
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Discrete measure
  • … identity and a convenient observable transfers from A canonical example satisfies the full defining rule of Discrete measure with every parameter and convention explicit. to A careful use of Discrete measure tests its carrier, assumptions, boundary and nearest confusable rather than relying on the label alone..
• Equivalence (measure theory)
  • Claims about stochastic-process laws, local equivalence, completions, or supporting measures require their additional index, filtration, and finiteness conventions.
• Measure space
  • The familiar abbreviation \((X,\mu)\) suppresses \(\Sigma\) only when context fixes it; it does not eliminate the sigma-algebra from the identity.
• Product measure
  • The entry treats standard nonnegative product measures; infinite products, signed measures, kernels, and disintegrations need additional existence and consistency hypotheses.
• Pushforward measure
  • The pushforward measure f_mu is defined by f_mu(B)=mu(f^{-1}(B)).
  • … example, the distinction between constitutive identity and a convenient observable transfers from The distribution of a random variable X is the pushforward of the underlying probability measure along X. to A calculation distinguishes image sets from preimages and uses the change-of-variables identity for integrals..
• Strictly positive measure
  • The property links topology and measure: it forbids an open region from being invisible to the measure, while still allowing individual points and many nonempty thin sets to have measure zero.
• Tau additivity
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Trivial measure
  • … distinction between constitutive identity and a convenient observable transfers from On any measurable space, mu(A)=0 for all A defines a complete finite measure with total mass zero. to A proof checks whether probability or strict-positivity assumptions exclude the trivial measure before using it as an edge case..

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