A note on the space of fuzzy measurable functions for a monotone measure

In this paper, we give a necessary and sufficient condition to guarantee that the space of all finite measurable functions for a monotonic measure is a topological vector space with a countable local base and in this space convergence with respect to this topology is equivalent to the convergence in...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 182; no. 1; pp. 2 - 12
Main Authors: Wu, Chong, Ren, Xuekun, Wu, Congxin
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 01.11.2011
Elsevier
Subjects:
Applied sciences
Circuit properties
Computer science; control theory; systems
Convergence
Digital circuits
Double asymptotic null-additivity
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Equivalence
Exact sciences and technology
Fuzzy
Fuzzy logic
Fuzzy measurable function
Fuzzy point
Fuzzy set theory
Information, signal and communications theory
Mathematical analysis
Mathematical methods
Mathematics
Measure and integration
Miscellaneous
Monotonic measure
Order continuity
Sciences and techniques of general use
Telecommunications and information theory
Theoretical computing
Topological vector space
Topology
Vector spaces
Double asymptotic null-additivity
Fuzzy measurable function
Fuzzy point
Monotonic measure
Order continuity
Topological vector space
Monotonic function
Fuzzy system
Necessary and sufficient condition
Vector measure
Fuzzy set
Convergence
Vector space
Information processing
ISSN:0165-0114, 1872-6801
Online Access:Get full text
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Description
Summary:In this paper, we give a necessary and sufficient condition to guarantee that the space of all finite measurable functions for a monotonic measure is a topological vector space with a countable local base and in this space convergence with respect to this topology is equivalent to the convergence in measure.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2010.10.006