Borel measure


Also found in: Wikipedia.

Borel measure

[bə′rel ‚mezh·ər]
(mathematics)
A measure defined on the class of all Borel sets of a topological space such that the measure of any compact set is finite.
References in periodicals archive ?
0]([OMEGA] x [OMEGA]'), there is a Borel measure [mu] on [OMEGA] x [OMEGA]' such that <u, x> = [[integral].
Let [mu] be a finite and positive Borel measure on the unit circle T = {z [member of] C, [absolute value of z] = 1}.
Our proof is obtained by the regularity properties of the corresponding regular Borel measure on [?
Let [mu] be a countably additive, regular, vector valued, Borel measure on R taking values in [B *.
The Borel measure [mu] which supported by K is defined by
Under certain assumptions on the finite Borel measure [mu] on [?
We introduce one notation on Borel measures: Let [mu] be a Borel measure on [R.
2][theta] defines a finite positive Borel measure [v.
Let [mu](x) be a positive and finite Borel measure with real support.
If [mu] is a finite and compactly supported Borel measure on the complex plane C, we denote by supp([mu]) its support, by
He covers the basic concepts, Gaussian measures, dynamical system, Borel product-measures, invariant Borel measures, quasi-invariant Radon measures, partial analogies of Lebegues measures, essential uniqueness, the Erdos-Sierpinski duality principle, strict transivity properties, invariant extensions of Haar measures, separated families of probability measures, an Ostrogradsky formula, and generalized Fourier series.