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L^/infinity functions   Message List  
Reply | Forward Message #358 of 455 |
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
Tue Feb 13, 2007 4:10 am

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gnavada
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Forward 		Message #358 of 455 |
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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
Offline Send Email 		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@...
Send Email 		Feb 13, 2007
5:22 pm

Quoting gnavada <gnavada@...>: It's false....
wilson@...
obscureveryo...
Offline Send Email 		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
Offline Send Email 		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
Offline Send Email 		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
Offline Send Email 		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
Offline Send Email 		Mar 4, 2007
3:17 am
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