Let ((X, mathscr{A}, mu)) be a measure space and (A_{1}, ldots, A_{N} in mathscr{A}) such that (muleft(A_{n}ight)

Question:

Let \((X, \mathscr{A}, \mu)\) be a measure space and \(A_{1}, \ldots, A_{N} \in \mathscr{A}\) such that \(\mu\left(A_{n}ight)<\infty\). Then

\[
\mu\left(\bigcup_{n=1}^{N} A_{n}ight) \geqslant \sum_{n=1}^{N} \mu\left(A_{n}ight)-\sum_{1 \leqslant n\]

[ show first an inequality for indicator functions.]

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question
Question Posted: