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 $\R^d$
Carathéodory's existence theorem, about the existence of solutions to ordinary differential equations
Carathéodory's extension theorem, about the extension of a measure
Carathéodory–Jacobi–Lie theorem, a generalization of Darboux's theorem in symplectic topology
Carathéodory's criterion, a necessary and sufficient condition for a measurable set
Carathéodory kernel theorem, a geometric criterion for local uniform convergence of univalent functions
Borel–Carathéodory theorem, about the boundedness of a complex analytic function
Vitali–Carathéodory theorem, a result in real analysis