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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2004 • Question 8

Question

Math 6010 • Linear Models 2004 • Question 8

If \(X\ge 0\) and \(X\in L^p(\mathbb {P})\) for all \(p>1\), then prove that \(\lim _{p\to \infty }\|X\|_p\) exists.

Raw LaTeX

If \(X\ge 0\) and \(X\in L^p(\Prob)\) for all \(p>1\), then prove that
\(\lim_{p\to\infty}\|X\|_p\) exists.

Topic Tags

Uniform Integrability and Truncation Methods