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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2005 • Question 5

Question

Math 6210 • Real Analysis 2005 • Question 5

Suppose \(f\) and \(g\) are two complex measurable functions on a measure space \(X\). Let \[ S=\{x\mid f(x)\ne g(x)\}. \] Prove or disprove: \(S\) is a measurable subset of \(X\).

Raw LaTeX

Suppose \(f\) and \(g\) are two complex measurable functions on a
measure space \(X\). Let
\[
S=\{x\mid f(x)\ne g(x)\}.
\]
Prove or disprove: \(S\) is a measurable subset of \(X\).

Topic Tags

Absolute Continuity and Singular Measures Measurable Functions Measure Theory Outer Measures and Caratheodory Measurability