Definition:Negative Part/Historical Note
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Definition
When Henri Lebesgue did the initial analysis on measurable functions, he was able to establish some useful results on positive functions.
In order to extend this theory to the general real-valued function and extended real-valued function, he took advantage of the fact that it is easier to split such a function into two parts: the positive part and the negative part.
Unfortunately for intuition, while defining the negative part he changed its sign to turn it into a positive function.