Caratheodory theorem

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• Borel–Carathéodory theorem — 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.… …   Wikipedia

• Vitali-Carathéodory theorem — noun A theorem which states that any real valued Lebesgue integrable function can be approached arbitrarily closely from below by an upper semicontinuous function and also from above by a lower semicontinuous function …   Wiktionary

• Carathéodory's theorem — In mathematics, Carathéodory s theorem may refer to one of a number of results of Constantin Carathéodory:* Carathéodory s theorem (convex hull) about the convex hulls of sets in Euclidean space *Carathéodory s theorem (measure theory) about… …   Wikipedia

• Carathéodory's criterion — is a result in measure theory that was formulated by Greek mathematician Constantin Carathéodory. Its statement is as follows: Let lambda^* denote the Lebesgue outer measure on mathbb{R}^n, and let Esubseteqmathbb{R}^n. Then E is Lebesgue… …   Wikipedia

• Carathéodory's extension theorem — See also Carathéodory s theorem for other meanings. In measure theory, Carathéodory s extension theorem proves that for a given set Ω, you can always extend a sigma; finite measure defined on R to the sigma; algebra generated by R , where R is a… …   Wikipedia

• Carathéodory's theorem (convex hull) — See also Carathéodory s theorem for other meanings In convex geometry Carathéodory s theorem states that if a point x of R d lies in the convex hull of a set P , there is a subset P prime; of P consisting of d +1 or fewer points such that x lies… …   Wikipedia

• Carathéodory's theorem (conformal mapping) — See also Carathéodory s theorem for other meanings. In mathematics, Carathéodory s theorem in complex analysis states that if U is a simply connected open subset of the complex plane C, whose boundary is a Jordan curve Γ then the Riemann map : f …   Wikipedia

• Caratheodory — Constantin Carathéodory (ca. 1920) Constantin Carathéodory (griechisch Κωνσταντίνος Καραθεοδωρή Konstantínos Karatheodorí; * 13. September 1873 in Berlin; † 2. Februar 1950 in München) war ein griechischer Mathematiker (in der Literatur findet …   Deutsch Wikipedia

• Carathéodory-Jacobi-Lie theorem — The Carathéodory Jacobi Lie theorem is a theorem in symplectic geometry which generalizes Darboux s theorem.tatementLet M be a 2 n dimensional symplectic manifold with symplectic form omega;. For p ∈ M and r le; n , let f 1, f 2, ..., f r be… …   Wikipedia

• Carathéodory conjecture — The Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger in a session of the Berlin Mathematical Society in 1924, [1] . Other early referencesare the presentation [3] of Stefan Cohn… …   Wikipedia

• Carathéodory, Constantin — ▪ German mathematician born Sept. 13, 1873, Berlin, Ger. died Feb. 2, 1950, Munich       German mathematician of Greek origin who made important contributions to the theory of real functions, to the calculus of variations, and to the theory of… …   Universalium