(Non-)Distributivity of the Product for $\sigma$-Algebras with Respect to the Intersection

• Main Author: Steinicke, Alexander
• Format: Journal Article
• Language: English
• Published: 12.07.2020
• Subjects: Mathematics - Functional Analysis; Mathematics - Probability

Arch. Math. (2021) We study the validity of the distributivity equation $$(\mathcal{A}\otimes\mathcal{F})\cap(\mathcal{A}\otimes\mathcal{G})=\mathcal{A}\otimes\left(\mathcal{F}\cap\mathcal{G}\right),$$ where $\mathcal{A}$ is a $\sigma$-algebra on a set $X$, and $\mathcal{F}, \mathcal{G}$ are $\sigma...