Some remarks concerning finitely subadditive outer measures with applications
type: Item
instance of: scholarly article
title: Some remarks concerning finitely subadditive outer measures with applications
zbMATH Open document ID: 0947.28003
DOI: 10.1155/S016117129800091X
author: John E. Knight
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1998-12-06T00:00:00Z
full work available at URL: https://eudml.org/doc/48545
review text: Summary: The present paper is intended as a first step toward the establishment of a general theory of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive outer measure and an associated finitely additive measure on any space is presented. This is followed by a discussion of the theory of inner measures, their construction, and the relationship of their properties to those of an associated finitely subadditive outer measure. In particular, the interconnections between the measurable sets determined by both the outer measure and its associated inner measure are examined. Finally, several applications of the general theory are given, with special attention being paid to various lattice related set functions.
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 28A10
zbMATH DE Number: 1230039
zbMATH Keywords: inner measure
zbMATH Keywords: measurable set
zbMATH Keywords: superadditive
zbMATH Keywords: submodular
zbMATH Keywords: supermodular
zbMATH Keywords: approximately regular
zbMATH Keywords: condition (M)
zbMATH Keywords: finitely subadditive outer measure
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1230039