Analysis- convergence of functions pointwise problem

Asked Oct 27 '13 at 17:13

Active Oct 27 '13 at 17:13

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Ok I HAVE COMPLETED THE FIRST PART, however for the second part with the restriction on fn(x) I cant find a sequence of functions (I can find a sequence of functions but the integral does converge to 0 unfortunately), im guessing after thinking about this there isnt a sequence of functions but I'm not sure how to prove this.

Thanks

asked Oct 27 '13 at 17:13

WhizKid

1

Think of the dominated convergence theorem. – Michael Greinecker Oct 27 '13 at 18:01
@MichaelGreinecker i havent come across that theorem before, would you say theorem is pretty conclusive in terms of how to solve the question above? – WhizKid Oct 27 '13 at 18:05
Yes, every solution to the second part will effectively bol down to using some form of it. – Michael Greinecker Oct 27 '13 at 18:08
@MichaelGreinecker is it possible you could possibly give me an example of such an function, so I could possibly see the shape- i will read about the theorem but its a theorem I wont be learning this year at uni – WhizKid Oct 27 '13 at 18:12
No, it is not possible for me to give an example of such a function. – Michael Greinecker Oct 27 '13 at 18:16
@MichaelGreinecker right so its not possible, ok I will try to construct a proof using the theorem. thanks – WhizKid Oct 27 '13 at 18:26
Are you self-studying the Cambridge Part IB? Good luck! – Willie Wong Oct 28 '13 at 09:14

Analysis- convergence of functions pointwise problem

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