III.18 Distributions, Terence Tao: Page 186

Analytic Functions – nice but sparse.  Examples include: exp, sin, polynomials.

Test functions.  Infinitely differentiable on closed interval [0,1].

Continuous functions.  Good for evaluation defined on [0,1].

Square integrable functions.

Borel measures.

Distributions.

Hyperfunctions.

Distributions as a weak limit of test functions.

Distributions are useful in the study of partial differential equations.

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