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)...

In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application...

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...

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

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...

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...

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

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)...

to a bona fide measure on a given space. Indeed, one of the fundamental theorems in measure theory states that a pre-measure can be extended to a measure...