Carathéodory's theorem

In mathematics, Carathéodory's theorem may refer to one of a number of results of Constantin Carathéodory:

• Carathéodory's theorem (conformal mapping), about the extension of conformal mappings to the boundary
• Carathéodory's theorem (convex hull), about the convex hulls of sets in Euclidean space
• Carathéodory's theorem (measure theory), about outer measures in measure theory
• Carathéodory's existence theorem, about the existence of solutions to ordinary differential equations
• Carathéodory's extension theorem, about the extension of a measure
• Borel–Carathéodory theorem, about the boundedness of a complex analytic function
• Carathéodory–Jacobi–Lie theorem, a generalization of Darboux's theorem in symplectic topology
• The Carathéodory kernel theorem, a geometric criterion for local uniform convergence of univalent functions