<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We discuss some basic ideas and survey some fundamental constructions related to measure (a real-valued map the domain of which is a set of measurable objects carrying a suitable structure and the map partially preserves the structure): continuity, measurability, duality, extension. We show that in the category <italic>ID </italic>of difference posets of fuzzy sets and sequentially continuous difference-homomorphisms these constructions are intrinsic. Further, basic notions of the probability theory have natural generalizations within <italic>ID</italic>.</p></abstract>

We discuss some basic ideas and survey some fundamental constructions related to measure (a real-valued map the domain of which is a set of measurable objects carrying a suitable structure and the map partially preserves the structure): continuity, measurability, duality, extension. We show that in the category ID of difference posets of fuzzy sets and sequentially continuous difference-homomorphisms these constructions are intrinsic. Further, basic notions of the probability theory have natural generalizations within ID.

Measures: continuity, measurability, duality, extension

Mathematical Institute Slovak Academy of Sciences Grešákova 6 SK–040-01 Košice SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"Measures: continuity, measurability, duality, extension"}

We discuss some basic ideas and survey some fundamental constructions related to measure (a real-valued map the domain of which is a set of measurable objects...

Measures: continuity, measurability, duality, extension

Online veröffentlicht: 12. Nov. 2012

Seitenbereich: 161 - 174

DOI: https://doi.org/10.2478/v10127-009-0015-8

Schlüsselwörter
bounded measure, sequential continuity, extension of measures, D-poset of fuzzy sets, bold algebra, Łukasiewicz tribe, measurable map, fuzzy random variable, observable, duality, probability measure, state, epireflection, generalized probability.

This content is open access.

Measures: continuity, measurability, duality, extension

Online veröffentlicht: 12. Nov. 2012

Seitenbereich: 161 - 174

DOI: https://doi.org/10.2478/v10127-009-0015-8

Schlüsselwörterbounded measure, sequential continuity, extension of measures, D-poset of fuzzy sets, bold algebra, Łukasiewicz tribe, measurable map, fuzzy random variable, observable, duality, probability measure, state, epireflection, generalized probability.

This content is open access.

Schlüsselwörter
bounded measure, sequential continuity, extension of measures, D-poset of fuzzy sets, bold algebra, Łukasiewicz tribe, measurable map, fuzzy random variable, observable, duality, probability measure, state, epireflection, generalized probability.