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Replies: 10   Last Post: Apr 25, 2013 1:01 PM

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 David C. Ullrich Posts: 3,555 Registered: 12/13/04
Posted: Apr 24, 2013 10:38 AM

On Wed, 24 Apr 2013 02:19:43 -0700, William Elliot <marsh@panix.com>
wrote:

>Assume for f:[0,1] -> R that there's some c /= 0,1 with
>for all x in [0,1/2], f(x) = c.f(2x).
>
>Show there's some k with for all x in [0,1], f(x) = kx.

Not true. It's well known that there exists a nowhere-
continuous function f : R -> R such that
f(x+y) = f(x) + f(y) for all x, y.

Maybe you omitted a hypothesis? Seems like it may be
true for continuous f...

Date Subject Author
4/24/13 William Elliot
4/24/13 David C. Ullrich
4/24/13 dan.ms.chaos@gmail.com
4/24/13 Herman Rubin
4/24/13 David C. Ullrich
4/25/13 David Petry
4/25/13 Herman Rubin
4/25/13 dan.ms.chaos@gmail.com
4/24/13 David C. Ullrich
4/24/13 William Elliot
4/25/13 David C. Ullrich