Borel measure


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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 ?
Let [mu] be a finite and positive Borel measure on the unit circle T = {z [member of] C, [absolute value of z] = 1}.
In [1], orthogonal rational functions with respect to a rational modification of a Borel measure on T are studied.
Our proof is obtained by the regularity properties of the corresponding regular Borel measure on [?
Considering [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we shall get an E-valued regular Borel measure [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ([7]) (we denote the measure j by the same notation as operator [?
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 [?
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.
1] (A) stand for the set of (say) unit Borel measures on A [subset] [R.