# UMD Analysis Qualifying Exam/Aug05 Real

## Problem 1

 Let ${\displaystyle f}$ be a bounded measurable function on ${\displaystyle R}$ for which there is a constant ${\displaystyle C}$ such that ${\displaystyle \forall \epsilon >0,m(x\in R:|f|>\epsilon ) Show that ${\displaystyle f\in L^{1}(R)}$.