The Carathéodory–Jacobi–Lie theorem is a theorem in symplectic geometry which generalizes Darboux's theorem. Let M be a 2n-dimensional symplectic manifold...

equations Carathéodory's extension theorem, about the extension of a measure Carathéodory–Jacobi–Lie theorem, a generalization of Darboux's theorem in symplectic...

Marius Sophus Lie (/liː/ LEE; Norwegian: [liː]; 17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous...

bidisc. He is credited with the Carathéodory extension theorem which is fundamental to modern measure theory. Later Carathéodory extended the theory from sets...

Carathéodory–Jacobi–Lie theorem Law of iterated expectations, or law of total expectation, initialized as LIE, a probability, statistical concept Lie...

(riemannian geometry) Bonnet theorem (differential geometry) Carathéodory–Jacobi–Lie theorem (symplectic topology) Cartan–Hadamard theorem (Riemannian geometry)...

chart. This theorem also holds for infinite-dimensional Banach manifolds. Carathéodory–Jacobi–Lie theorem, a generalization of this theorem. Moser's trick...

identity Carathéodory–Jacobi–Lie theorem Desnanot–Jacobi identity Euler–Jacobi pseudoprime Euler–Jacobi problem Gauss–Jacobi quadrature Hamilton–Jacobi equation...

Hamilton–Jacobi equations for the sub-Riemannian Hamiltonian are called geodesics, and generalize Riemannian geodesics. Carnot group, a class of Lie groups...

Sophus Lie. Sophus Lie (1842 – 1899), a mathematician, is the eponym of all of the things (and topics) listed below. Carathéodory–Jacobi–Lie theorem Lie algebra...

the Lie bracket [ X , Y ] {\displaystyle [X,Y]} . It is skew-symmetric [ X , Y ] = − [ Y , X ] {\displaystyle [X,Y]=-[Y,X]} and satisfies the Jacobi identity:...

uniqueness theorems are usually important organizational principles. In many introductory textbooks, the role of existence and uniqueness theorems for ODE...

introductory probability textbook Giovanni Carandino (1784–1834) Constantin Carathéodory (1873–1950) - Mathematician who pioneered the Axiomatic Formulation of...

calculus of variations had related ideas (e.g., the work of Caratheodory, the Hamilton-Jacobi equation). This led to conflicts with the calculus of variations...