
Re: AskanAnalysis problem
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...

