𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Boolean algebras: Convergence and measure

✍ Scribed by Roman Frič

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
115 KB
Volume
111
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

✦ Synopsis

We study topological and categorical aspects of the extension of σ -additive measures from a field of sets to the generated σ -field within a category of Boolean algebras carrying initial sequential convergences with respect to 2-valued homomorphisms. We describe the relationship between σadditivity and sequential continuity of finitely additive measures. A key role is played by the epireflective subcategory of absolutely sequentially closed objects. In case of fields of sets such objects are exactly σ -fields. The results provide information about basic notions of probability theory: events, probability measures, and random functions.

📜 SIMILAR VOLUMES

Special subsets of cf(μ)μ, Boolean algeb
Special subsets of cf(μ)μ, Boolean algebras and Maharam measure algebras
✍ Saharon Shelah 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 792 KB

The original theme of the paper is the existence proof of "there is η = η α : α < λ which is a (λ, J )-sequence for Ī = I i : i < δ , a sequence of ideals". This can be thought of as a generalization to Luzin sets and Sierpinski sets, but for the product i<δ dom(I i ), the existence proofs are relat

Closure Algebras and Boolean Algebras
Closure Algebras and Boolean Algebras
✍ G. J. Logan 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 212 KB

## S(z A y ) z S(A), by (c) * S(z) A S(Y) 2 S(A) e S(x) 2 S(A) and S(y) 2 S(A) e C ( s ) s C ( A ) 'and C ( y ) E C ( A ) , by (c) o x € C ( A ) and Y E C ( A ) . Now every ultrafilter is consistent and closed with respect to C, since if U is an ultrafilter and C ( U ) = X , then C({,uu,, . . ., ,