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...

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

invariants Darboux or Goursat problem Darboux transformation Darboux vector Darboux's problem Darboux's theorem in symplectic geometry Darboux's theorem in real...

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

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

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

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

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

analysis) Darboux's theorem (real analysis) Denjoy–Carleman theorem (functional analysis) Denjoy-Young-Saks theorem (real analysis) Dini's theorem (analysis) Divergence...

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;...

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

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

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...

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}...

lower/upper Darboux sums of f {\displaystyle f} and upper/lower Darboux sums of f − 1 {\displaystyle f^{-1}} . The antiderivative version of the theorem then...

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 the...

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

Maclaurin used it to calculate integrals. It was later generalized to Darboux's formula. If m and n are natural numbers and f(x) is a real or complex...

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

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...

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

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...

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

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

Heisenberg group also occurs in Fourier analysis, where it is used in some formulations of the Stone–von Neumann theorem. In this case, the Heisenberg group...

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

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...

an effort to avoid naming everything after Euler, some discoveries and theorems are attributed to the first person to have proved them after Euler. Euler's...

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...

the Newlander–Nirenberg theorem in complex geometry. He is regarded as a foundational figure in the field of geometric analysis, with many of his works...