Displaying similar documents to “Orlicz spaces of finitely additive set functions”

Representations of bimeasures

Kari Ylinen (1993)

Studia Mathematica

Similarity:

Separately σ-additive and separately finitely additive complex functions on the Cartesian product of two algebras of sets are represented in terms of spectral measures and their finitely additive counterparts. Applications of the techniques include a bounded joint convergence theorem for bimeasure integration, characterizations of positive-definite bimeasures, and a theorem on decomposing a bimeasure into a linear combination of positive-definite ones.

On abstract Stieltjes measure

James E. Huneycutt Jr. (1971)

Annales de l'institut Fourier

Similarity:

In 1955, A. Revuz - Annales de l’Institut Fourier, vol. 6 (1955-56) - considered a type of Stieltjes measure defined on analogues of half-open, half-closed intervals in a partially ordered topological space. He states that these functions are finitely additive but his proof has an error. We shall furnish a new proof and extend some of this results to “measures” taking values in a topological abelian group.

Theory of the integral

Stanisław Saks

Similarity:

CONTENTS PREFACE...................... III ERRATA.......................... VII CHAPTER I. The integral in an abstract space § 1. Introduction.................................. 1 § 2. Terminology and notation...................... 4 § 3. Abstract space X.............................. 6 § 4. Additive classes of sets...................... 7 § 5. Additive functions of a set................... 8 § 6. The variations of an additive function........ 10 § 7. Measurable functions.............................