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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2021 • Question 1

Question

Math 6210 • Real Analysis Fall 2021 • Question 1

Let \((X, \mathcal {M})\) be a measurable space, so that \(\mathcal {M}\) is a \(\sigma \)-algebra of subsets of \(X\). Prove that \(\mathcal {M}\) is either finite or uncountable.

Raw LaTeX

Let \((X, \mathcal{M})\) be a measurable space, so that \(\mathcal{M}\) is a \(\sigma\)-algebra of subsets
of \(X\). Prove that \(\mathcal{M}\) is either finite or uncountable.

Topic Tags

Borel Sets and Sigma-Algebras Measurable Functions