Intereting Posts

How can I prove the formula for calculating successive entries in a given row of Pascal's triangle?
Probability of Gambler's Ruin with Unequal Gain/Loss
Evaluation of $\sum^{\infty}_{n=0}\frac{1}{16^n}\binom{2n}{n}.$
Prove $\varphi\in\mathcal{S}(\mathbb R^n)$ if and only if the following inequality holds..
Group of order $p^2+p $ is not simple
how many semantically different boolean functions are there for n boolean variables?
$p$ prime, $1 \le k \le p-2$ there exists $x \in \mathbb{Z} \ : \ x^k \neq 0,1 $ (mod p)
Exponential of a polynomial of the differential operator
$\lfloor (2+\sqrt{3})^n \rfloor $ is odd
Should I understand a theorem's proof before using the theorem?
How many elements in a number field of a given norm?
Sum Involving Bernoulli Numbers : $\sum_{r=1}^n \binom{2n}{2r-1}\frac{B_{2r}}{r}=\frac{2n-1}{2n+1}$
Does finite projective dimension localize?
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
Clarification regarding white space in rules of inference

A $T$-invariant sub-sigma algebra of $\mathcal{B}$ where $(X,\mathcal{B},\mu,T)$ is a measure-preserving system is a collection $\mathcal{A}$ of elements of $\mathcal{B}$ that forms a sigma-algebra itself and satisfies $T^{-1}\mathcal{A} = \mathcal{A}$ mod $\mu$, meaning $\forall A \in \mathcal{A} \hspace{1mm} \exists B \in \mathcal{A}$ such that $\mu(T^{-1}A\Delta B) = 0$.

A problem I am working on discusses the smallest T-invariant sub-sigma algebra satisfying a certain property. The existence of such a thing presumably is based on the fact that the arbitrary intersection of $T$-invariant sub-sigma algebras is itself a sub-sigma algebra. This fact is clear to me if the definition were instead that $T^{-1}\mathcal{A} = \mathcal{A}$, without the mod $\mu$. However, since the intersection might be over an uncountable index, I do not see the proof or reason why this fact should be true with the “mod $\mu$” present.

Any help is appreciated.

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