- #1
the_dane
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Homework Statement
Suppose E1 and E2 are a pair of compact sets in Rd with E1 ⊆ E2, and let a = m(E1) and b=m(E2). Prove that for any c with a<c<b, there is a compact set E withE1 ⊆E⊆E2 and m(E) = c.
Homework Equations
m(E) is ofcourese referring to the outer measure of E
The Attempt at a Solution
I know that for d=1 measurable subset of [0,1]. Is it worth it to look at the measure m(E∩[0,t]) as function of t?
I really don't know how to tackle this one