3. Prove that if E has finite measure and let {f,}be a sequence of measurable functions on E thatconverges pointwise a.e. on E to f and f is finite a.e. on E. Then{fn}→f in measure on E.***end***ND.

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Answered: 3. Prove that if E has finite measure…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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3. Prove that if E has finite measure and let {f.}be a sequence of measurable functions on E that converges pointwise a.e. on E to f and f is finite a.e. on E. Then{f„}→f in measure on E.