We study topological and categorical aspects of the extension of Ο -additive measures from a field of sets to the generated Ο -field within a category of Boolean algebras carrying initial sequential convergences with respect to 2-valued homomorphisms. We describe the relationship between Οadditivity
Metric Boolean algebras and constructive measure theory
β Scribed by Thierry Coquand; Erik Palmgren
- Publisher
- Springer
- Year
- 2002
- Tongue
- English
- Weight
- 142 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0933-5846
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π SIMILAR VOLUMES
## Abstract In conventional generalization of the main results of classical measure theory to Stone algebra valued measures, the values that measures and functions can take are Booleanized, while the classical notion of a Οβfield is retained. The main purpose of this paper is to show by abundace of
## Abstract Some aspects of the theory of Boolean algebras and distributive latticesβin particular, the Stone Representation Theorems and the properties of filters and idealsβare analyzed in a constructive setting.
The original theme of the paper is the existence proof of "there is Ξ· = Ξ· Ξ± : Ξ± < Ξ» which is a (Ξ», J )-sequence for Δͺ = I i : i < Ξ΄ , a sequence of ideals". This can be thought of as a generalization to Luzin sets and Sierpinski sets, but for the product i<Ξ΄ dom(I i ), the existence proofs are relat