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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2011 • Question 2

Question

Math 6210 • Real Analysis Spring 2011 • Question 2

Let \(f\) be a real-valued function on a measure space \(X\). Prove or disprove the following statements:

(a) If \(f\) is measurable, then so is \(|f|\).

(b) If \(|f|\) is measurable, then so is \(f\).

Raw LaTeX

Let \(f\) be a real-valued function on a measure space \(X\). Prove
or disprove the following statements:

(a) If \(f\) is measurable, then so is \(|f|\).

(b) If \(|f|\) is measurable, then so is \(f\).

Topic Tags

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