In mathematics, Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that every function that results from the differentiation...

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

In mathematical analysis, the intermediate value theorem states that if f {\displaystyle f} is a continuous function whose domain contains the interval...

problem Darboux transformation Darboux vector Darboux's problem Darboux's theorem in symplectic geometry Darboux's theorem in real analysis, related...

theorem (cellular automata) Cut-elimination theorem (proof theory) Dandelin's theorem (solid geometry) Danskin's theorem (convex analysis) Darboux's theorem...

distinguished from complex analysis, which deals with the study of complex numbers and their functions. The theorems of real analysis rely on the properties...

partial results such as Darboux's theorem and the Cartan-Kähler theorem. Despite being named for Ferdinand Georg Frobenius, the theorem was first proven by...

– gives the Taylor series of the inverse of an analytic function Darboux's theorem – states that all functions that result from the differentiation of...

the curvature provides a local invariant of Riemannian manifolds, Darboux's theorem states that all symplectic manifolds are locally isomorphic. The only...

In mathematics, the Christoffel–Darboux formula or Christoffel–Darboux theorem is an identity for a sequence of orthogonal polynomials, introduced by Elwin...

differentiable. ATS theorem Carleson's theorem Dirichlet kernel Discrete Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier sine...

as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations. It is an application of the divergence theorem, and it relates...

a c between a and b such that f(c) = y. This is a consequence of Darboux's theorem. The set of discontinuities of f must be a meagre set. This set must...

this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides...

applications, the Riemann integral can be evaluated by the fundamental theorem of calculus or approximated by numerical integration, or simulated using...

In the mathematical field of analysis, a well-known theorem describes the set of discontinuities of a monotone real-valued function of a real variable;...

F'(x)=f(x)} for every x ∈ I {\displaystyle x\in I} . According to Darboux's theorem, the derivative function f : I → R {\displaystyle f:I\to \mathbb {R}...

x_{0}} . f ′ {\displaystyle \displaystyle f'} does not skip values (by Darboux's theorem), so it has to be zero at some point between the positive and negative...

countable, so f is zero almost everywhere. In fact, the de Bruijn–Post Theorem states the converse of the above criterion: If f is a function such that...

but does not treat material such as Fubini's theorem. Rudin, Walter (1966). Real and complex analysis. New York: McGraw-Hill Book Co. pp. xi+412. MR 0210528...

work on integer partitions, starting in 1918, first using a Tauberian theorem and later the circle method. Walter Hayman's 1956 paper "A Generalisation...

Bertrand–Edgeworth model – Economic Model Bertrand curve Buckingham π theorem – Theorem in dimensional analysis Struik, D.J. (1970–1980). "Bertrand, Joseph Louis Francois"...

Nevertheless, Darboux's theorem implies that the derivative of any function satisfies the conclusion of the intermediate value theorem. Similarly to how...

Fourier's theorem on polynomial real roots, published in 1820. François Budan, in 1807 and 1811, had published independently his theorem (also known...

integral, and an invaluable tool in unifying equivalent forms of statistical theorems that apply to discrete and continuous probability. The Riemann–Stieltjes...

The non-squeezing theorem, also called Gromov's non-squeezing theorem, is one of the most important theorems in symplectic geometry. It was first proven...

kind of integral. In the context of Riemann integrals (or, equivalently, Darboux integrals), this typically involves unboundedness, either of the set over...

choose coordinates so as to make the symplectic structure constant, by Darboux's theorem; and, using the associated Poisson bivector, one may consider the...

centers of force. Special cases of these generalized problems include Darboux's problem and Velde's problem. Euler's three-body problem is to describe...

engineering. SLPs are also useful in the analysis of certain partial differential equations. There are several theorems that establish existence and uniqueness...