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Are Ugly Functions Measurable?
Автор: MathGems
Загружено: 2021-05-30
Просмотров: 113
Описание:
In this video we show that a non-continuous solution of the functional equation f(x+y)=f(x)+f(y) can not be a measurable function. This implies that if a measurable function satisfies the functional equation f(x+y)=f(x)+f(y) then f must be continuous and hence, there exists a real constant c such that f(x)=cx for all real x.
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