Is there $U\subset \Bbb R^2$ with Lebesgue measure $0$ such that
$$f(x+y)=f(x)+f(y)$$ for all $(x, y)\in U$ implies $f(x+y)=f(x)+f(y)$ for all $(x, y)\in\Bbb R^2$ ?
I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...
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