Measure, Integration & Real Analysis · Problem 2A.8

Measures — Sheldon Axler

Mathematics — Measure Theory · outer-measure-decomposition

Problem

Prove that if A⊆RA \subseteq \mathbf{R} and t>0t > 0, then ∣A∣=∣A∩(−t,t)∣+∣A∩(R∖(−t,t))∣|A| = |A \cap (-t, t)| + \left|A \cap \bigl(\mathbf{R} \setminus (-t, t)\bigr)\right|.

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