In mathematics, Carathéodory's theorem may refer to one of a number of results of Constantin Carathéodory:
Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ...
In measure theory, Carathéodory's extension theorem (named after the mathematician Constantin Carathéodory) states that any pre-measure defined on a given ring of subsets R of a given set Ω can be extended to a measure on the σ-ring generated by...
In mathematics, Carathéodory's existence theorem says that an ordinary differential equation has a solution under relatively mild conditions. It is a generalization of Peano's existence theorem. Peano's theorem requires that the right-hand side of...
In mathematics, Carathéodory's theorem is a theorem in complex analysis, named after Constantin Carathéodory, which extends the Riemann mapping theorem. The theorem, published by Carathéodory in 1913, states that any conformal mapping sending the...
In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer...
Constantin Carathéodory (Greek: Κωνσταντίνος Καραθεοδωρή, romanized: Konstantinos Karatheodori; 13 September 1873 – 2 February 1950) was a Greek mathematician who spent most of his professional career in Germany. He is the author of significant...
In mathematics, the Vitali–Carathéodory theorem is a result in real analysis that shows that, under the conditions stated below, integrable functions can be approximated in L1 from above and below by lower- and upper-semicontinuous functions,...
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 the maximum modulus principle. It is named for Émile Borel and Constantin Carathéodory.
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.