On the setwise convergence of sequences of signed topological measures

Svistula, Marina Genad'evna

doi:10.1007/s00013-013-0485-4

Cited by 2 publications

(3 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 29. Signed topological measures of finite norm on a compact space were introduced in [10] then studied or used in [11], [13], [16], [18].…”

Section: Signed Topological Measures On a Locally Compact Spacementioning

confidence: 99%

“…The study of topological measures (initially called quasi-measures) be-deficient topological measures. Signed topological measures of finite norm on a compact space were introduced in [10] then studied and used in various works, including [11], [13], [16], and [18]. Deficient topological measures (as real-valued functions on a compact space) were first defined and used by A. Rustad and O. Johansen in [13] and later independently rediscovered and further developed by M. Svistula in [16] and [17].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Signed Topological Measures on Locally Compact Spaces

Butler

2019

Anal Math

View full text Add to dashboard Cite

In this paper we define and study signed deficient topological measures and signed topological measures (which generalize signed measures) on locally compact spaces. We prove that a signed deficient topological measure is τ -smooth on open sets and τ -smooth on compact sets. We show that the family of signed measures that are differences of two Radon measures is properly contained in the family of signed topological measures, which in turn is properly contained in the family of signed deficient topological measures. Extending known results for compact spaces, we prove that a signed topological measure is the difference of its positive and negative variations if at least one variation is finite; we also show that the total variation is the sum of the positive and negative variations. If the space is locally compact, connected, locally connected, and has the Alexandroff one-point compactification of genus 0, a signed topological measure of finite norm can be represented as a difference of two topological measures.2010 Mathematics Subject Classification. Primary 28C15; Secondary 28C99. Key words and phrases. signed deficient topological measure; signed topological measure; positive, negative, total variation of a signed deficient topological measure.

show abstract

“…Remark 29. Signed topological measures of finite norm on a compact space were introduced in [10] then studied or used in [11], [13], [16], [18].…”

Section: Signed Topological Measures On a Locally Compact Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Signed Topological Measures on Locally Compact Spaces

Butler

2019

Anal Math

View full text Add to dashboard Cite

show abstract

“…The natural generalizations of topological measures are signed topological measures and deficient topological measures. Signed topological measures of finite norm on a compact space were introduced in [10] then studied and used in various works, including [11], [14], [17], and [19]. Deficient topological measures (as real-valued functions on a compact space) were first defined and used by A. Rustad and ∅.…”

mentioning

confidence: 99%

Decompositions of signed deficient topological measures

Butler¹

2019

Preprint

View full text Add to dashboard Cite

This paper focuses on various decompositions of topological measures, deficient topological measures, signed topological measures, and signed deficient topological measures. These set functions generalize measures and correspond to certain non-linear functionals. They may assume ∞ or −∞. We introduce the concept of a proper signed deficient topological measure and show that a signed deficient topological measure can be represented as a sum of a signed Radon measure and a proper signed deficient topological measure. We also generalize practically all known results that involve proper deficient topological measures and proper topological measures on compact spaces to locally compact spaces. We prove that the sum of two proper (deficient) topological measures is a proper (deficient) topological measure. We give a criterion for a (deficient) topological measure to be proper.

show abstract

On the setwise convergence of sequences of signed topological measures

Cited by 2 publications

References 4 publications

Signed Topological Measures on Locally Compact Spaces

Signed Topological Measures on Locally Compact Spaces

Decompositions of signed deficient topological measures

Contact Info

Product

Resources

About