harmonicanalysis : Message: Re: [harmonic] L^/infinity functions

harmonicanalysis · Harmonic Analysis

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Message #361 of 456 |

Re: [harmonic] L^/infinity functions

Hai,

I think that is not true in general. Particular you can visualise this by taking a step function on a bounded interval.

bye....

wilson@... wrote:

Quoting gnavada <gnavada@yahoo.com>:

It's false.

> Hello,
> I need a proof of the following fact: L^/infinity functions in R can
> be made continuous by changing the values of functions on a set of
> measure zero. Even a reference to the proof will help.
> thanks
> gowri
>
>

D.VENKU NAIDU,
CAUVERY HOSTEL,
ROOM NO:2045,
IIT,MADRAS,
CHENNAI-36

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Wed Feb 14, 2007 4:18 am

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Message #361 of 456 |

Expand Messages	Author	Sort by Date
Hello, I need a proof of the following fact: L^/infinity functions in R can be made continuous by changing the values of functions on a set of measure zero....	gnavada	Feb 13, 2007 5:15 pm
What you want is not true. The fact you mean is that you can do it with a set of arbitrary small measure....	Maria Roginskaya maria@...	Feb 13, 2007 5:22 pm
Quoting gnavada <gnavada@...>: It's false....	wilson@... obscureveryo...	Feb 13, 2007 6:11 pm
Hai, I think that is not true in general. Particular you can visualise this by taking a step function on a bounded interval. bye.... wilson@... wrote:...	venku naidu venku_uoh	Feb 14, 2007 4:29 am
Hi Thanks. I got similar mails from others saying it is not true. I havnt checked a counterexample yet, but I'll do it. In page 192 of Rudin's "Real and...	Gowri Navada gnavada	Feb 14, 2007 3:57 pm
Hi Gowri, Look at equation (5) on pg. 192. We assumed, that \phi(f) is not zero and that \beta(y) is in L^\infinity. On the other hand, since the map f \to f_y...	Bela A. Frigyik frigyik	Feb 14, 2007 7:35 pm
Hi Gowri; I think the best you can do in approximating such function is Lusin's Theorem, which is sometimes very useful. Anyways, here I provide a counter...	zaher_hani	Mar 4, 2007 3:17 am

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