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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2019 • Question 2

Question

Math 6210 • Real Analysis Spring 2019 • Question 2

Let \((X,\mathcal M,\mu )\) be a measure space. Assume there exists \(\delta >0\) such that for every \(E\in \mathcal M\), either \(\mu (E)=0\) or \(\mu (E)>\delta \). Let \(f\in L^1(X)\). Prove that \(f\) is essentially bounded.

Raw LaTeX

Let \((X,\mathcal M,\mu)\) be a measure space. Assume there exists
\(\delta>0\) such that for every \(E\in\mathcal M\), either \(\mu(E)=0\) or
\(\mu(E)>\delta\). Let \(f\in L^1(X)\). Prove that \(f\) is essentially bounded.

Topic Tags

Absolute Continuity and Singular Measures Isolated Singularities and Residues Lp Spaces and Sequence Spaces Measure Theory