Tuesday, 28 April 2015

Cauchy's functional equation real to real

Cauchy's functional equation:
f(x+y)=f(x)+f(y)
On wikipedia (and some other websites) it says that there are non-linear solutions for real to real. But I don't quite understand about additive functions and Lebesgue measure.Can someone give me an example of a non-linear solution and explain the set of non-linear solutions throughly?



Thank you in advance.

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