What is Carathéodory's extension theorem?

In mathematics, the Lagrange reversion theorem gives series or formal power series expansions of certain implicitly defined functions; indeed, of compositions with such functions. Let v be a function of...

The fundamental theorem of algebra, also known as d'Alembert's theorem, or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This...

In mathematics, the Poincaré–Hopf theorem is an important theorem that is used in differential topology. It is named after Henri Poincaré and Heinz Hopf. The Poincaré–Hopf theorem is often illustrated...

In mathematics, more specifically in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem is a result giving an explicit description of the universal enveloping algebra of a Lie algebra. It...

In symplectic topology and dynamical systems, Poincaré–Birkhoff theorem states that every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed...

In functional analysis, it is often convenient to define a linear transformation on a complete, normed vector space X...

Carathéodory's criterion is a result in measure theory that was formulated by Greek mathematician Constantin Carathéodory that characterizes when a set is Lebesgue measurable.

The M. Riesz extension theorem is a theorem in mathematics, proved by Marcel Riesz during his study of the problem of moments.

In functional analysis, the Friedrichs extension is a canonical self-adjoint extension of a non-negative densely defined symmetric operator. It is named after the mathematician Kurt Friedrichs. This extension is particularly...