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This exercise is a partial converse to Exercise 1.5.13. Let $X$ be a probability space, and let $f_n: X \rightarrow \mathbf{C}$ be a sequence of absolutely integrable functions with $\sup _n\left\|f_n\right\|_{L^1}<\infty$.

   This exercise is a partial converse to Exercise 1.5.13. Let $X$ be a probability space, and let $f_n: X \rightarrow \mathbf{C}$ be a sequence of absolutely integrable functions with $\sup _n\left\|f_n\right\|_{L^1}<\infty$.

An Introduction To Measure Theory (January 2011 Draft)

Terence Tao 1st Edition

Chapter 1, Problem 14

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This exercise is a partial converse to Exercise 1.5.13. Let $X$ be a probability space, and let $f_n: X \rightarrow \mathbf{C}$ be a sequence of absolutely integrable functions with $\sup _n\left\|f_n\right\|_{L^1}<\infty$.

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