Comment by 082349872349872
1 month ago
Do I understand properly that in a different universe distributions could have been called prefunctions?
1 month ago
Do I understand properly that in a different universe distributions could have been called prefunctions?
A distribution is a function, on the space of test functions.
OK, so if we have a distribution D (less nice than the average function) and a test function T (nicer than the average function), we have ⟨D,T⟩ = c: ℂ, so ⟨D,—⟩: test fn→ℂ and ⟨—,T⟩: distribution→ℂ ?
Wait i thought functions are predistributions..
[My bad, it was Matvei, not Manuel, no idea how i mixed that up..
Checkout his childrens books, as well as
https://archive.is/eaYRs
Note how the independent diagonals are what i consider interesting]
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A distribution is not a function. It is a continuous linear functional on a space of functions.
Functions define distributions, but not all distributions are defined that way, like the Dirac delta or integration over a subset.
A functional is a function.
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Try composing two distributions.
Try composing f : A -> B with g : A -> B, for A ≠ B. Still, f and g are functions. So, what exactly is your point?
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