In measure theory, Carathéodory's extension theorem (named after the mathematician Constantin Carathéodory) states that any pre-measure defined on a given...

In mathematics, Carathéodory's theorem may refer to one of a number of results of Constantin Carathéodory: Carathéodory's theorem (conformal mapping)...

measures are for example used in the proof of the fundamental Carathéodory's extension theorem), and was used in an essential way by Hausdorff to define a...

Carathéodory's theorem is a theorem in complex analysis, named after Constantin Carathéodory, which extends the Riemann mapping theorem. The theorem,...

of them are nonzero. With the lemma, Carathéodory's theorem is a simple extension: Proof of Carathéodory's theorem For any x ∈ C o n v ( S ) {\displaystyle...

Extension theorem may refer to: Carathéodory's extension theorem - a theorem in measure theory, named after the Greek mathematician Constantin Carathéodory...

lower than the one provided by Carathéodory's theorem can be obtained. He is credited with the authorship of the Carathéodory conjecture claiming that a closed...

The maximal product measure can be constructed by applying Carathéodory's extension theorem to the additive function μ such that μ(A × B) = μ1(A)μ2(B)...

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

construction of the Lebesgue measure is an application of Carathéodory's extension theorem. It proceeds as follows. Fix n ∈ N. A box in Rn is a set of...