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The study of definable sets and functions in polish spaces.

A test for the convergence of Fourier series. Let phi_x(t)=f(x+t)+f(x-t)-2f(x), then if int_0^pi(|phi_x(t)|dt)/t is finite, the Fourier series converges to f(x) at x.

Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...

Let (X,B,mu) be a measure space and let E be a measurable set with mu(E)<infty. Let {f_n} be a sequence of measurable functions on E such that each f_n is finite almost ...

Ellipsoidal calculus is a method for solving problems in control and estimation theory having unknown but bounded errors in terms of sets of approximating ellipsoidal-value ...

A singular point a for which f(z)(z-a)^n is not differentiable for any integer n>0.

A topology arising from a sheaf of continuous functions. It derives a natural topology from the projection operator. Etale spaces are examples of space that are not T2.

The ring of fractions of an integral domain. The field of fractions of the ring of integers Z is the rational field Q, and the field of fractions of the polynomial ring ...

The curvature and torsion functions along a space curve determine it up to an orientation-preserving isometry.

The computer animation format MPEG-7 uses Gabor functions to specify texture descriptors.