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Among the continuous functions on R^n, the positive definite functions are those functions which are the Fourier transforms of nonnegative Borel measures.

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general ...

For a smooth harmonic map u:M->N, where del is the gradient, Ric is the Ricci curvature tensor, and Riem is the Riemann tensor.

The converse of Fisher's theorem.

There are several theorems that generally are known by the generic name "Pappus's Theorem." They include Pappus's centroid theorem, the Pappus chain, Pappus's harmonic ...

Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...

The reciprocity theorem for x^8=q (mod p).

There are so many theorems due to Fermat that the term "Fermat's theorem" is best avoided unless augmented by a description of which theorem of Fermat is under discussion. ...

R^n is homeomorphic to R^m iff n=m. This theorem was first proved by Brouwer.

The two-dimensional version of the ham sandwich theorem.