! Let ECR. Show that E is Lebesgue measurable if and only if there exists a sequence of open sets (Un)-1 such that E C Un for all n and |(~²) x6 = 0. Un E n=1
! Let ECR. Show that E is Lebesgue measurable if and only if there exists a sequence of open sets (Un)-1 such that E C Un for all n and |(~²) x6 = 0. Un E n=1
! Let ECR. Show that E is Lebesgue measurable if and only if there exists a sequence of open sets (Un)-1 such that E C Un for all n and |(~²) x6 = 0. Un E n=1
Transcribed Image Text:2.
Let ECR. Show that E is Lebesgue measurable if and only
if there exists a sequence of open sets (Un)‰=1 such that E ≤ Un for all
n and
|(1₁) 12-0
Un E
= 0.
Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.
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