A measurable function between measurable spaces

Depends on

• Measurable spaces and measurable sets

Used by

• Higher-dimensional simple symmetric walks are transient Corollary
• One-dimensional simple symmetric walk is recurrent Corollary
• Two-dimensional simple symmetric walk is recurrent Corollary
• An orientation-reversing homeomorphism need not be quasiconformal Counterexample
• A simple function and its canonical representation Definition
• Borel functional calculus for a bounded normal operator Definition
• Borel measurable and Lebesgue measurable functions on ℝⁿ Definition
• Direct integral of a measurable Hilbert field Definition
• Measurable and decomposable operator fields Definition
• Measurable Hilbert field from a countable fundamental family Definition
• Measure kernel and probability kernel Definition
• Measure-preserving transformations and systems Definition
• Random elements and real random variables Definition
• Sections Eₓ, Eʸ, fₓ, and fʸ on a product Definition
• Spectral multiplicity function in the separable case Definition
• Systems of imprimitivity for a Borel G-space Definition
• The sigma-algebra generated by a function Definition
• Uniformly elliptic divergence-form operators and their sesquilinear forms Definition
• Gambler’s ruin from harmonicity Example
• Green kernel of a biased integer walk Example
• Multiplicity-two diagonal representation Example
• Negative drift gives a finite mean small-set hit Example
• Newton shell theorem from harmonic mean values Example
• Pvm of a multiplication operator Example
• The positive-type Gaussian on the real line and its cyclic model Example
• Absolute real powers are Borel measurable and convex Lemma
• Conull Borel uniformizations and Borel versions of measured suprema Lemma
• Diagonal multipliers form a von Neumann algebra Lemma
• Ergodic systems with regular orbits concentrate on one orbit Lemma
• Følner nets give Reiter nets Lemma
• Measurable dense selections for fields of nonempty compact sets Lemma
• Measurable Gram-Schmidt and constant-field trivializations on dimension strata Lemma
• Measurable sections have measurable pointwise inner products Lemma
• Operators commuting with a generating family of multiplications Lemma
• Reiter functions can be cut down to Følner sets Lemma
• Steinhaus and Pettis: Borel homomorphisms of second-countable locally compact groups are continuous Lemma
• The elliptic form is well defined and bounded on H¹ Lemma
• The layer-cake identity for integrable functions Lemma
• The truncated Riesz kernel is bounded on Lᵖ of a bounded set Lemma
• Weighted monomial integrals and monomial norms for the disc, ball and polydisc Lemma

…and 12 more results.

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Sheldon Axler, Measure, Integration and Real Analysis, Section 2B (standard reference, not scraped)
• John K. Hunter, Measure Theory, Definition 3.1 (standard reference, not scraped)