Measures: continuity, measurability, duality, extension

Roman Frič

doi:10.2478/v10127-009-0015-8

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Measures: continuity, measurability, duality, extension

Tatra Mountains Mathematical Publications

Volume 42 (2009): Issue 1 (April 2009)

By: Roman Frič

Open Access

|Nov 2012

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.

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