What are the Reasons for the Ambiguous Meaning of “Distribution” in Mathematics

The term "distribution" is commonly associated with statistics and, less commonly known, to generalized functions.

Questions:

• what is known about the origin of the term in the two fields?
• are the terms related in some sense i.e. were the distributions in the context of generalized functions inspired by the distributions of statistics or is the one an analogue or generalization of the other?
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Besides probability-distributions and schwartz-distributions, you've missed tangent-distributions in your enumeration. –  Willie Wong Feb 3 at 11:45
@WillieWong, I didn't miss it - I didn't know of it; thanks for mentioning it, I will look it up. –  Manfred Weis Feb 3 at 12:23
As I see it, the presence in mathematics of general terms with various meanings, such as "distribution" of "field", and adjectives like "normal" and "regular", is generally due to the fact that the mathematical language seeks for simplicity. Also note that at the time when these terms were introduced, different fields used to be more separated, and there were no danger of confusion. –  Pietro Majer Feb 3 at 15:34
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1 Answer

The name "distributions" for generalized functions is explained by Laurent Schwartz in his autobiography "A Mathematician Grappling with His Century", p. 238 : he chose the name "Because, if $\mu$ is a measure, i.e. a particular kind of distribution, it can be considered as a distribution of electric charges in the universe. Distributions give more general types of electric charges, for example dipoles and magnetic distributions (...)".

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