Radon measure on an LCH space

Depends on

• The Borel sigma-algebra of a topological space
• Measures on sigma-algebras
• Open cover, subcover, and compact topological space; a compact subset is a subspace that is compact in its own right

Used by

• Normalised positive definite functions correspond to probability measures Corollary
• The obstacle reaction is supported on the contact set under measure regularity Corollary
• LCA Fourier inversion is not an everywhere statement for arbitrary L¹ functions Counterexample
• The complementarity product needs extra regularity Counterexample
• Harmonic measure on a bounded regular plane domain Definition
• Left Haar integral and left Haar measure Definition
• Left, right, and bi-invariant Borel measures Definition
• Logarithmic potential and energy of a positive compactly supported measure Definition
• Regular Borel measure on an LCH space Definition
• Spectral measures and the known-mean periodogram Definition
• States, tracial states and faithful normal traces on a von Neumann algebra Definition
• Support of a finite Borel measure on the plane Definition
• A character is positive definite Example
• An atomic sinusoid and an AR(1) process have different spectra Example
• Haar measure on an infinite product of compact groups Example
• Haar normalisations on a finite abelian group and its dual Example
• Haar normalisations on the circle and the integers Example
• Multiplicity-two diagonal representation Example
• Property (T) for finite groups via normalized counting measure Example
• Riesz measure of a log modulus records the holomorphic zeros Example
• The modular function of the affine group of the line Example
• Weighted counting in dimension zero Example
• Every Borel measure on an LCH space is Radon False statement
• Inner regularity on open sets implies inner regularity on all Borel sets False statement
• A topological invariant mean yields norm-approximately invariant densities Lemma
• A transitive Borel G-space with a quasi-invariant measure class is ergodic Lemma
• Compact-open neighbourhoods on the dual give a neighbourhood basis on the group Lemma
• Counting measure on a discrete group is Haar, Haar measures there are its multiples, and integrals against them are sums Lemma
• Finite Haar mass, compact detection, and integrable pairings Lemma
• Fourier-Stieltjes transforms determine finite Radon measures Lemma
• Fourier-Stieltjes transforms of positive measures are continuous positive definite Lemma
• Haar measure is positive on nonempty open sets and finite on compact sets Lemma
• Haar measure on an abelian group is invariant under inversion Lemma
• Haar null classes and Borel descent on a homogeneous space Lemma
• L¹ of an LCA group is a commutative Banach star algebra under convolution Lemma
• Probability-density approximation of continuous tests and topological means Lemma
• Quadratic path energy is lower semicontinuous Lemma
• Reiter functions can be cut down to Følner sets Lemma
• Scalar unitisation of L¹ of an LCA group: characters, spectrum and identity criterion Lemma
• Smooth compactly supported tests are dense for finite Radon L2 measures Lemma

…and 31 more results.

Dependency tree · two levels

13 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

• Donald L. Cohn, Measure Theory, 2nd ed., §7.2 (standard reference, not scraped)