A Radon-Nikodym theorm for Stone algebra valued measures

A Radon-nikodym Theorem for Stone Algebra Valued Measures

Introduction. Let C(S) be the ring of continuous real valued functions on a compact Hausdorff space S. Stone [5] shows that each bounded subset of C(S) has a least upper bound (in C(S)) if and only if the closure of each open subset of S is open ; in this event we call C(S) a Stone algebra. Throughout this paper C(S) is a Stone algebra. It is convenient to adjoin an object +00, not in C(S), and...

Reasonable non–Radon–Nikodym idealss

For any abelian Polish σ-compact group H there exist an Fσ ideal Z ⊆ P (N) and a Borel Z -approximate homomorphism f : H → HN which is not Z -approximable by a continuous true homomorphism g : H → HN .

A Radon-Nikodym approach to measure information

A Reformulation of the Radon-nikodym Theorem

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

A Radon-Nikodym derivative for almost subadditive set functions

In classical measure theory, the Radon-Nikodym theorem states in a concise condition, namely domination, how a measure can be factorized by another (bounded) measure through a density function. Several approaches have been undertaken to see under which conditions an exact factorization can be obtained with set functions that are not σ-additive (for instance finitely additive set functions or su...