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{{about|an extension of the theory of the [[Lebesgue integral]] to [[manifold]]s|numerical method|geometric integ ...ion''' or '''geometric integration''' is a method for extending the notion of the [[integral]] to [[manifold]]s. Rather than functions or [[differential ...

...ons'', Doctoral. Thesis, [[Tokyo Institute of Technology]]</ref> is a type of integral with respect to a [[fuzzy measure theory|fuzzy measure]]. The Sugeno integral over the crisp set <math>A \subseteq X</math> of the function <math>h</math> with respect to the fuzzy measure <math>g</math ...

.... The integral also permits analogues of the chain rule and other theorems of the integral calculus for higher dimensions. ...The Riemann sums of the Pfeffer integral are taken over partitions made up of such sets, rather than intervals as in the Riemann or Henstock integrals. A ...

...a correspondence''' is a generalization of the [[Integral | integration]] of [[Function (mathematics)|single-valued functions]] to [[ Set-valued functio ...sen |editor3-link=James Heckman |editor4-link=Rosa Matzkin |title=Handbook of Econometrics, vol. 7 |date=2020 |publisher=Elsevier |isbn=9780444636492 |pa ...

{{Short description|Extension of the classical tensor calculus}} ...:Dannebrog.jpg|thumb|200px|The surface of a flag in the wind is an example of a deforming manifold.]] ...

{{Short description|Integral in integration theory}} ...s of Lebesgue, Denjoy, Perron, and Henstock |date=1994 |publisher=American Mathematical Society |isbn=0-8218-3805-9 |location=Providence, R.I. |pages=157–163 |oclc ...

{{Short description|Family of functions}} ...Society |page=90 }}</ref> but sometimes the definition of an approximation of the identity is taken to be the same as for a summability kernel. ...

...expansion of n-dimensional Faxén-type integrals |journal=European Journal of Pure and Applied Mathematics |volume=3 |number=6 |date=2010 |pages=1006–103 ...cation to the generalised Faxén integral |journal=Methods and Applications of Analysis |volume=4 |date=1997 |issue=3 |pages=311–325 |doi=10.4310/MAA.1997 ...

...The term causality refers to the adaptation to the [[natural filtration]] of the integrator. ...\mathbf{F}^W=\{\mathcal{F}_t^W, t\geq 0\}</math> be the natural filtration of the Wiener process, ...

...limit function]] ₀''F''₁ of one variable. The first of these double series was introduced by {{harvs|txt|authorlink=Pierre Humbert ==Definitions== ...

...tegral]] of a [[function (mathematics)|function]]. It is a generalization of the [[Riemann integral|Riemann]] and [[Lebesgue integral|Lebesgue]] integra ...arv | Bruckner | 1994 | loc=chapter 5, §2 }}</ref> by the derivative ''g'' of the (differentiable but not absolutely continuous) function ''f''(''x'') = ...

...culus]], an '''iterated limit''' is a [[limit of a sequence]] or a [[limit of a function]] in the form ...variables. To evaluate such a limit, one takes the limiting process as one of the two variables approaches some number, getting an expression whose value ...

{{Short description|Type of integral}} ...functional analysis]], '''double operator integrals''' (DOI) are integrals of the form ...

...equations : analysis and numerical solution |date=2006 |publisher=European Mathematical Society |isbn=978-3-03719-017-3}}</ref> == Definitions == ...

...liy Skorokhod]] and [[Japan]]ese mathematician [[Masuyuki Hitsuda]]. Part of its importance is that it unifies several concepts: * <math>\delta</math> is an extension of the [[Itô integral]] to non-[[adapted process]]es; ...

{{Short description|Mathematical object}} ...polytopes: Their definition, generation and aggregate properties |journal=Mathematical Programming |date=December 1982 |volume=24 |issue=1 |pages=39–54 |doi=10.10 ...

{{Short description|Measure that has a notion of derivative}} ...itle=Differentiable Measures and the Malliavin Calculus|journal=Journal of Mathematical Sciences|volume=87|pages=3577–3731|publisher=Springer|isbn=978-0821849934}} ...

{{Short description|Definite integral of a scalar or vector field along a path}} ...a [[curve]].<ref name="Tang2006">{{cite book|author=Kwong-Tin Tang| title=Mathematical Methods for Engineers and Scientists 2: Vector Analysis, Ordinary Different ...

...roach to the Kontsevich Quantization Formula | journal = Communications in Mathematical Physics | volume = 212 | issue = 3 | pages = 591–611 | doi = 10.1007/s00220 ==Deformation quantization of a Poisson algebra== ...

...Chow group of ''X'' is the same as the ''G''-'''equivariant Chow group''' of ''Y''. ...-theoretic operations must take this into account. For example, the degree of a 0-cycle on a stack need not be an integer but is a rational number (due t ...