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An upper semicontinuous function whose restrictions to all complex lines are subharmonic (where defined). These functions were introduced by P. Lelong and Oka in the early ...

A positive measure is a measure which is a function from the measurable sets of a measure space to the nonnegative real numbers. Sometimes, this is what is meant by measure, ...

A pseudoanalytic function is a function defined using generalized Cauchy-Riemann equations. Pseudoanalytic functions come as close as possible to having complex derivatives ...

That portion of mathematics dealing with functions of real variables. While this includes some portions of topology, it is most commonly used to distinguish that portion of ...

The real axis is the line in the complex plane corresponding to zero imaginary part, I[z]=0. Every real number corresponds to a unique point on the real axis.

If pi on V and pi^' on V^' are irreducible representations and E:V|->V^' is a linear map such that pi^'(g)E=Epi(g) for all g in and group G, then E=0 or E is invertible. ...

Let f be analytic on the unit disk, and assume that 1. |f(z)|<=1 for all z and 2. f(0)=0. Then |f(z)|<=|z| and |f^'(0)|<=1. If either |f(z)|=|z| for some z!=0 or if ...

The set St^_v-Stv, where St^_v is a closed star and Stv is a star, is called the link of v in a simplicial complex K and is denoted Lkv (Munkres 1993, p. 11).

Let K be a T2-topological space and let F be the space of all bounded complex-valued continuous functions defined on K. The supremum norm is the norm defined on F by ...

A branch point of an analytic function is a point in the complex plane whose complex argument can be mapped from a single point in the domain to multiple points in the range. ...