In measure theory, Carathéodory's extension theorem (named after the mathematician Constantin Carathéodory) states that any pre-measure defined on a given...
15 KB (2,612 words) - 08:16, 12 September 2024
In mathematics, Carathéodory's theorem may refer to one of a number of results of Constantin Carathéodory: Carathéodory's theorem (conformal mapping)...
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Outer measure (redirect from Carathéodory's theorem (measure theory))
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...
19 KB (2,471 words) - 01:25, 14 July 2024
Carathéodory's theorem is a theorem in complex analysis, named after Constantin Carathéodory, which extends the Riemann mapping theorem. The theorem,...
14 KB (2,064 words) - 07:17, 4 June 2024
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...
14 KB (2,153 words) - 21:04, 8 July 2024
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...
43 KB (4,812 words) - 07:40, 23 September 2024
Extension theorem may refer to: Carathéodory's extension theorem - a theorem in measure theory, named after the Greek mathematician Constantin Carathéodory...
2 KB (224 words) - 19:16, 5 September 2018
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)...
41 KB (7,845 words) - 06:53, 6 September 2024
Carathéodory's criterion is a result in measure theory that was formulated by Greek mathematician Constantin Carathéodory that characterizes when a set...
3 KB (458 words) - 01:33, 5 November 2023
Lebesgue measure (redirect from Regularity theorem for Lebesgue measure)
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...
18 KB (2,641 words) - 00:30, 11 September 2024