Measure, Integration & Real Analysis · Problem 4A.5

Product Measures — Sheldon Axler

Mathematics — Measure Theory · vitali-covering-lemma-inclusion

Problem

Prove the assertion left as an exercise in the last sentence of the proof of the Vitali Covering Lemma (4.4). [The assertion is: if

|I_{k_L}| \geq |I_j|

and

I_{k_L} \cap I_j \neq \emptyset

, then

I_j \subseteq 3 * I_{k_L}