σ-finite. Combining Fubini's theorem with Tonelli's theorem gives the Fubini–Tonelli theorem. Often just called Fubini's theorem, it states that if X...
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Distribution (mathematics) (redirect from Fubini's theorem for distributions)
{\displaystyle f,g,\phi \in {\mathcal {D}}(\mathbb {R} ^{n}),} then by Fubini's theorem ⟨ C f g , ϕ ⟩ = ∫ R n ϕ ( x ) ∫ R n f ( x − y ) g ( y ) d y d x = ⟨...
128 KB (21,614 words) - 07:27, 10 August 2024
In mathematics, Fubini's theorem on differentiation, named after Guido Fubini, is a result in real analysis concerning the differentiation of series of...
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Guido Fubini (19 January 1879 – 6 June 1943) was an Italian mathematician, known for Fubini's theorem and the Fubini–Study metric. Born in Venice, he was...
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used as a type of transfinite induction to prove many other theorems, such as Fubini's theorem. A monotone class is a family (i.e. class) M {\displaystyle...
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Fubini (1879–1943), Italian mathematician Sergio Fubini (1928–2005), Italian theoretical physicist It can also be used to refer to Fubini's theorem....
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Another example is closely related to the failure of some forms of Fubini's theorem for spaces that are not σ-finite. Suppose that X {\displaystyle X}...
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integrands under certain conditions. This property is popularly known as Fubini's theorem. In the case of T ⊆ R 2 {\displaystyle T\subseteq \mathbb {R} ^{2}}...
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In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is...
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Fubini's nightmare is a seeming violation of Fubini's theorem, where a nice space, such as the square [ 0 , 1 ] × [ 0 , 1 ] , {\displaystyle [0,1]\times...
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algebras) Froda's theorem (mathematical analysis) Frucht's theorem (graph theory) Fubini's theorem (integration) Fubini's theorem on differentiation...
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g ∈ L 1 ( R n ) {\displaystyle f,g\in L^{1}(\mathbb {R} ^{n})} , Fubini's theorem implies that ∫ g ( ξ ) ⋅ ( F f ) ( ξ ) d ξ = ∫ ( F g ) ( y ) ⋅ f (...
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theorem, introduced by Kazimierz Kuratowski and Stanislaw Ulam (1932), called also the Fubini theorem for category, is an analog of Fubini's theorem for...
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mathematics, Tonelli's theorem may refer to Tonelli's theorem (measure theory), a successor of Fubini's theorem Tonelli's theorem (functional analysis)...
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with respect to the supremum norm. Morera's theorem can also be used in conjunction with Fubini's theorem and the Weierstrass M-test to show the analyticity...
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y)=c\,} satisfies Mercer's condition, as then the integral becomes by Fubini's theorem ∬ g ( x ) c g ( y ) d x d y = c ∫ g ( x ) d x ∫ g ( y ) d y = c ( ∫...
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Symmetry of second derivatives (redirect from Young's Theorem)
positive if F is positive. The equality above is a simple case of Fubini's theorem, involving no measure theory. Titchmarsh (1939) proves it in a straightforward...
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Cavalieri's principle (redirect from Cavalieri's theorem)
and while it is used in some forms, such as its generalization in Fubini's theorem and layer cake representation, results using Cavalieri's principle...
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Differential form (section Stokes's theorem)
this integral is the integral of the function f(t) on the interval. Fubini's theorem states that the integral over a set that is a product may be computed...
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calculate areas and volumes of regions in the plane and in space. Fubini's theorem guarantees that a multiple integral may be evaluated as a repeated...
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Schwarz's theorem Interchange of integrals: Fubini's theorem Interchange of limit and integral: Dominated convergence theorem Vitali convergence theorem Fichera...
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transforms iterated integrals (or multiple integrals through the use of Fubini's theorem) of functions into other, hopefully simpler, integrals by changing...
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Ordered Bell number (redirect from Fubini number)
total order. Their alternative name, the Fubini numbers, comes from a connection to Guido Fubini and Fubini's theorem on equivalent forms of multiple integrals...
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Gaussian integral (category Theorems in analysis)
_{-a}^{a}e^{-\left(x^{2}+y^{2}\right)}\,dy\,dx.\end{aligned}}} Using Fubini's theorem, the above double integral can be seen as an area integral ∬ [ − a...
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Integral (section Fundamental theorem of calculus)
the domain R. Under suitable conditions (e.g., if f is continuous), Fubini's theorem states that this integral can be expressed as an equivalent iterated...
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_{\left\{h(X)=1\right\}}]\end{aligned}}} where the second line was derived through Fubini's theorem Notice that R ( h ) {\displaystyle R(h)} is minimised by taking ∀ x...
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fact that integrals are preserved by inversion of the domain, and by Fubini's theorem. Young's inequality can also be proved by interpolation; see the article...
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f on (a,b) the function Iα f on (a,b) which is also integrable by Fubini's theorem. Thus Iα defines a linear operator on L1(a,b): I α : L 1 ( a , b )...
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In terms of null sets, the following equivalence has been styled a Fubini's theorem: For A ⊂ R 2 {\displaystyle A\subset \mathbb {R} ^{2}} and A x = {...
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integrals over the level sets of another function. A special case is Fubini's theorem, which says under suitable hypotheses that the integral of a function...
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