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.