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There are at least two integrals called the Poisson integral. The first is also known as Bessel's second integral, ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

Two complex measures mu and nu on a measure space X, are mutually singular if they are supported on different subsets. More precisely, X=A union B where A and B are two ...

Given a complex measure mu, there exists a positive measure denoted |mu| which measures the total variation of mu, also sometimes called simply "total variation." In ...

Let x and y be vectors. Then the triangle inequality is given by |x|-|y|<=|x+y|<=|x|+|y|. (1) Equivalently, for complex numbers z_1 and z_2, ...

If a, b, c, and d are points in the extended complex plane C^*, their cross ratio, also called the cross-ratio (Courant and Robbins 1996, p. 172; Durell 1928, p. 73), ...

A generalization of Fermat's last theorem which states that if a^x+b^y=c^z, where a, b, c, x, y, and z are any positive integers with x,y,z>2, then a, b, and c have a common ...

A coloring of plane regions, link segments, etc., is an assignment of a distinct labeling (which could be a number, letter, color, etc.) to each component. Coloring problems ...

The first Morley triangle DeltaA^'B^'C^', also simply known as "Morley's triangle", is the triangle constructed from pairwise intersections of the angle trisectors of a given ...

The volume of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as V=1/6sum_(i=1)^Na_i·n_i, where the normal n_i ...