Lebesgue measure, prooving that a specific open set exists

[bobby2k]

Homework Statement

Homework Equations

The Attempt at a Solution

I have managed to solve it for the finite case, where the masure is less than infinity. But how do I solve it if the ,measure if the measure of E is infinite?

 

[Dick]

Homework Statement

View attachment 79135

Homework Equations

The Attempt at a Solution

I have managed to solve it for the finite case, where the masure is less than infinity. But how do I solve it if the ,measure if the measure of E is infinite?

Solve it on intersections of intervals with E with small enough values of epsilon that you can sum them all and get the original epsilon.