- #1

Bashyboy

- 1,421

- 5

## Homework Statement

Let ##E## be a nonmeasurable set of finite outer measure. Show that there is a ##G_\delta## set ##G## that contains ##E## for which ##m^*(E)=m^*(G)##, while ##m^*(G-E) > 0##.

## Homework Equations

##E## is a measurable set if and only if there is a ##G_\delta## set ##G## containing ##E## for which ##m^*(G-E)=0##.

Let ##E## have finite outer measure. Show that there is an ##F_\sigma## set ##F## and a ##G_\delta## set ##G## such that ##F \subseteq E \subseteq G## and ##m^*(F)=m^*(E)=m^*(G)##.

## The Attempt at a Solution

I pretty certain it wouldn't follow immediately from the two theorems I quoted in section 2, right? In fact, we could prove an analogous theorem for ##F_\sigma## sets, right?