Measurability Proof

Thu 28 January 2016

Filed under math

Note: I can't finish this till I get Dr Ov's book so I can use Thm 2.4i, 2.4iii, 2.48

Prove that a function $f $on $[a,b]$ is measurable iff $f$ inverse($U$) is measurable for any open set $U$ of $R$.

$\Rightarrow$ \newline By Theorem 2.4i, and Theorem 2.4iii, we have 2 open sets: \newline $ J = { x: f(x) k } ,$ where $j c \right}$ is measurable. \newline By Theorem 2.48, $f$ is measurable.

Measurability Proof

Prove that a function $f $on $[a,b]$ is measurable iff $f$ inverse($U$) is measurable for any open set $U$ of $R$.

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