Let {fn} be a sequence of nonnegative measurable functions and fn (x) → f (x) on a set A of finite measure and gn (x) = min (g (x), fn (x)), where is a bounded measurable which vanishes outside a set A. Moreover, g < f. a) Give a rigorous proof (using e and Ne notations) of fact that gn (x) → g (x) for each x E A.b) Does a) allow us to conclude that lim fp 9n = Se g? If it is not the case, explain why? 2. Let {fn} be a sequence of nonnegative measurable functions andfn (x) → f (x) on a set A of finite measure and gn (x) = min (g (x), fn (x)),where g is a bounded measurable which vanishes outside a set A.Morcover, g < f.a) Give a rigorous proof (using e and Ne notations) of factthat gn (x) -b) Does a) allow us to conclude that lim/p InIf it is not the case, explain why?g (x) for each x E A.= SE 9?

Let fn be a sequence of nonnegative measurable functions. Given that fn→f on a set A of finite…

Answered: 2. Let {fn} be a sequence of…

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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Let {fn} be a sequence of nonnegative measurable functions and fn (x) → f (x) on a set A of finite measure and gn (x) = min (g (x), fn (x)), where is a bounded measurable which vanishes outside a set A. Moreover, g < f. a) Give a rigorous proof (using e and Ne notations) of fact that gn (x) → g (x) for each x E A.b) Does a) allow us to conclude that lim fp 9n = Se g? If it is not the case, explain why?

2. Let {fn} be a sequence of nonnegative measurable functions and
fn (x) → f (x) on a set A of finite measure and gn (x) = min (g (x), fn (x)),
where g is a bounded measurable which vanishes outside a set A.
Morcover, g < f.
a) Give a rigorous proof (using e and Ne notations) of fact
that gn (x) -
b) Does a) allow us to conclude that lim/p In
If it is not the case, explain why?
g (x) for each x E A.
= SE 9?

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