Given a sequence of functions $\{f_n\}$, $|f_n(x)|<\infty$ a.e. x. Why does the measure $m\{x\in [0,1]: |f_n(x)| \geq 1\}\leq 1$

Question

I am reading a proof, but I couldn't understand the circled part. Can someone help me to understand why $m(F_1) \leq 1$?

score 2 · Accepted Answer · answered Mar 07 '18 at 23:22

2

Simply because $\{x\in[0,1]: |f_{n}(x)|\geq 1\}\subseteq[0,1]$ and the Lebesgue measure of the interval is $1$.

answered Mar 07 '18 at 23:22

user284331

1

Thank you. I understand it now. It's a measure of a subset of $[0,1]$. – user398843 Mar 07 '18 at 23:25

1 Answers1