Arithmetic of (independent) sigma-fields on probability spaces

TL;DR

This paper reviews and extends the understanding of operations like intersection, generation, and complementation of independent complete sigma-fields on probability spaces, offering new insights into their algebraic properties.

Contribution

It provides new results and consolidates existing knowledge on the algebraic operations involving independent complete sigma-fields.

Findings

New results on intersection and complementation of sigma-fields

Enhanced understanding of generated sigma-fields

Clarification of properties of independent sigma-fields

Abstract

This note gathers what is known about, and provides some new results concerning the operations of intersection, of ``generated $\sigma$-field'', and of ``complementation'' for (independent) complete $\sigma$-fields on probability spaces.