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The Darboux integral, also called a Darboux-Stieltjes integral, is a variant of the Stieltjes integral that is defined as a common value for the lower and upper Darboux ...

A partially ordered set (or ordered set or poset for short) (L,<=) is called a complete lattice if every subset M of L has a least upper bound (supremum, supM) and a greatest ...

The generalized diameter is the greatest distance between any two points on the boundary of a closed figure. The diameter of a subset E of a Euclidean space R^n is therefore ...

Let F be the set of complex analytic functions f defined on an open region containing the closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each f in ...

A Banach space X is called prime if each infinite-dimensional complemented subspace of X is isomorphic to X (Lindenstrauss and Tzafriri 1977). Pełczyński (1960) proved that ...

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 ...

A topological space that contains a homeomorphic image of every topological space of a certain class. A metric space U is said to be universal for a family of metric spaces M ...

Let F be the set of complex analytic functions f defined on an open region containing the set closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each ...

The complementary subspace problem asks, in general, which closed subspaces of a Banach space are complemented (Johnson and Lindenstrauss 2001). Phillips (1940) proved that ...

Let G be a Lie group and let rho be a group representation of G on C^n (for some natural number n), which is continuous in the sense that the function G×C^n->C^n defined by ...