UMD Analysis Qualifying Exam/Aug05 Real

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Problem 1[edit]

Let f be a bounded measurable function on R for which there is a constant C such that

\forall \epsilon >0, m(x \in R : |f|>  \epsilon) < C/\sqrt{\epsilon}

Show that f \in L^1(R).

Solution 1[edit]

Problem 3[edit]

Solution 3[edit]

Problem 5[edit]

Solution 5[edit]