Some Properties of Complete Boolean Algebras
The main result of this paper is a characterization of the strongly algebraically closed algebras in the lattice of all real-valued continuous functions and the equivalence classes of $\lambda$-measurable. We shall provide conditions which strongly algebraically closed algebras carry a strictly po...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2021-05-01
|
| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_242304_dd36edfbe215f4011e11996eac789ce2.pdf |
| Summary: | The main result of this paper is a characterization of the strongly algebraically closed algebras in the lattice of all real-valued continuous functions and the equivalence classes of $\lambda$-measurable. We shall provide conditions which strongly algebraically closed algebras carry a strictly positive Maharam submeasure. Particularly, it is proved that if $B$ is a strongly algebraically closed lattice and $(B,\, \sigma)$ is a Hausdorff space and $B$ satisfies the $G_\sigma$ property, then $B$ carries a strictly positive Maharam submeasure. |
|---|---|
| ISSN: | 2322-5807 2423-3900 |