1. Let f be bounded measurable function on E. Show that there are sequence of simple functions on E, {φn} and {ψn}, such that {φn} is increasing and {ψn} is decreasing and each of these sequences converges to f uniformly on E 2. A real valued measurable function is said to be semisimple provided it takes only a countable number of values. Let f be any measurable function on E. Show that there is a sequence of semisimple functions {fn} on E that converges to f uniformly on E

1. Let f be bounded measurable function on E. Show that there are sequence of simple functions on E, {φn} and {ψn}, such that {φn} is increasing and {ψn} is decreasing and each of these sequences converges to f uniformly on E 2. A real valued measurable function is said to be semisimple provided it takes only a countable number of values. Let f be any measurable function on E. Show that there is a sequence of semisimple functions {fn} on E that converges to f uniformly on E

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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