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May I raise you a

https://en.m.wikipedia.org/wiki/Distribution_function

It's right in the title.

In probability theory, integration theory, as well as electrical engineering, "distribution function", unless further clarified, means that cumulative thing.

In math, nomenclature overloading can be a problem. So context matters. In the context of dirac delta, distribution means something else entirely -- generalized functions.

Oh! So sad you deleted your point about densities. One can only laugh at and enjoy these idiosyncrasies of nomenclature.

In Electrical Engineering one uses j for imaginary numbers because i is taken (by current).



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