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

Measures — Sheldon Axler

Mathematics — Measure Theory · borel-sets-smallest-sigma-algebra-example

Problem

Verify that the smallest

\sigma

-algebra on

\mathbf{R}

containing

\mathcal{A} = \{(0,1),(0,\infty)\}

\{\varnothing, (0,1),(0,\infty),(-\infty,0]\cup[1,\infty),(-\infty,0],[1,\infty),(-\infty,1),\mathbf{R}\}