- #1

joypav

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**Problem:**

Let $E$ be a subset of $R$ with $m^∗(E) < ∞$, and let $K$ be a collection of compact intervals $I$ covering $E$. Show that there exists a positive constant $β$ and a finite number of disjoint intervals $I_1, . . . , I_N$ in $K$ such that

$$\sum_{n=1}^N |I_n| ≥ β \cdot m^∗(E)$$Could someone help me out here? I'm guessing this is an application of the Vitali Covering theorem? I'm not sure how to apply it. However, I will keep working and edit if I get somewhere.