# touchstone principle – Is intersection of two product \$sigma\$-algebras is too a product \$sigma\$-algebra? Answer

Hello expensive customer to our community We will proffer you an answer to this query touchstone principle – Is intersection of two product \$sigma\$-algebras is too a product \$sigma\$-algebra? ,and the respond will breathe typical by way of documented data sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning concerning the respond to this query.

touchstone principle – Is intersection of two product \$sigma\$-algebras is too a product \$sigma\$-algebra?

Given a quadruple of measurable areas $$(A,mathcal{A})$$,
$$(A,mathcal{A}’)$$, $$(B,mathcal{B})$$, $$(B,mathcal{B}’)$$ is it
undoubted that
$$mathcal{A}otimesmathcal{B}capmathcal{A}’otimesmathcal{B}’$$
is too a product of some $$sigma$$-algebras on $$A$$ and $$B$$? I
would speculate the respond is “no”, however how would one inform that an
$$sigma$$-algebra $$mathcal{C}$$ on $$Atimes B$$ is just not a product, aside from the
trifling “too few cylinder-sets”?

we’ll proffer you the answer to touchstone principle – Is intersection of two product \$sigma\$-algebras is too a product \$sigma\$-algebra? query through our community which brings all of the solutions from a number of dependable sources.