In this paper we derive the analogue of the Lebesque-Radon-Nikodym theorem with respect to fermionic p-adic invariant measure on Zp. 2010 Mathematics Subject Classification : 11S80, 48B22, 28B99

In this paper we clarify the relation between inverse systems, the Radon-Nikodym property, the Asymptotic Norming Property of James-Ho [JH81], and the GFDA spaces introduced in [CK06].

The Radon-Nikodym theorems of Segal and Zaanen are principally concerned with the classification of those measures p. for which any X« p. is given in the form

That is, a smooth one-parameter family of measurable hypersurfaces may be translated to lie in a null set. Moreover, the translations may be taken parallel to R and need not depend on g. Our motivation came from studying curved analogues of the Kakeya and Nikodym problems: we wished to show that a null set could contain a translate of every member of a specified family of curves, or in the Niko...

Let (S,Σ , μ) be a complete positive σ -finite measure space and let X be a Banach space. We are concerned with the proximinality problem for the best simultaneous approximations to two functions in L p(S,Σ , X). Let Σ0 be a sub-σ -algebra of Σ and Y a nonempty locally weakly compact convex subset of X such that span Y and its dual have the Radon–Nikodym property. We prove that L p(S,Σ0, Y ) is...

Conditional expectation is one of the most useful tools of probability. The Radon-Nikodym theorem enables us to construct conditional expectations. Definition 1. A measure µ on (Ω, F) is σ-finite iff there is A n ∈ F satisfying A n ↑ Ω where µ(A n) < ∞ for all n. Definition 2. Let µ, ν be measures on (Ω, F). Then ν is absolutely continuous with respect to µ (ν << µ) iff for all A ∈ F, µ(A) = 0 ...

In this talk basic general properties of f -divergences, including their axiomatic, and some important classes of f -divergences are presented. Without essential loss of insight we restrict ourselves to discrete probability distributions and note that the extension to the general case relies strongly on the Lebesgue-Radon-Nikodym Theorem.

Recently, Jensen [3], Lazar [4] and Rothwell [6] have investigated in detail the structure of scattered C*-algebras which can be regarded as the most elementary generalization of the finite dimensional involutive algebras. A C*-algebra si is called scattered if every positive functional of si is the sum of a sequence of pure functionals. The object of this note is to give a short proof of a nat...