On the transform of a singular or an absolutely continuous measure

An Approximation of the Hankel Transform for Absolutely Continuous Mappings

Using some techniques developed by Dragomir and Wang in the recent paper [2] in connection to Ostrowski integral inequality, we point out some approximation results for the Henkel’s transform of absolutely continuous mapping.

Indistinguishability of Absolutely Continuous and Singular Distributions

It is shown that there are no consistent decision rules for the hypothesis testing problem of distinguishing between absolutely continuous and purely singular probability distributions on the real line. In fact, there are no consistent decision rules for distinguishing between absolutely continuous distributions and distributions supported by Borel sets of Hausdorff dimension 0. It follows that...

An Approximation for the Fourier Transform of Absolutely Continuous Mappings

The Fourier Transform is an important mathematical tool in a wide variety of fields of science and engineering [1, p. XI]. In this paper, by the use of some integral identities and inequalities developed in [2](see also [3]), we point out some approximations of the Fourier transform in terms of the complex exponential mean, E (z, w) (see Section 2) and study the error of approximation for diffe...

Exchangeable Sequences Driven by an Absolutely Continuous Random Measure

Let S be a Polish space and (Xn : n ≥ 1) an exchangeable sequence of S-valued random variables. Let αn(·) = P ( Xn+1 ∈ · | X1, . . . , Xn ) be the predictive measure and α a random probability measure on S such that αn weak −→ α a.s.. Two (related) problems are addressed. One is to give conditions for α λ a.s., where λ is a (non random) σ-finite Borel measure on S. Such conditions should concer...

On Absolutely Continuous Transformations