In mathematics, the Bochner integral, named for Salomon Bochner, extends the definition of Lebesgue integral to functions that take values in a Banach space, as the limit of integrals of simple functions.
In mathematics, the Bochnerintegral, named for Salomon Bochner, extends the definition of Lebesgue integral to functions that take values in a Banach...
The integral is also called the weak integral in contrast to the Bochnerintegral, which is the strong integral. Let f : X → V {\displaystyle f:X\to V}...
Choquet integral, a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953. The Bochnerintegral, an extension...
identity arguments. In 1933 he defined the Bochnerintegral, as it is now called, for vector-valued functions. Bochner's theorem on Fourier transforms appeared...
: 13–15 Other integrals can be approximated by versions of the Gaussian integral. Fourier integrals are also considered. The first integral, with broad...
notions of weak and strong measurability agree when B is separable. BochnerintegralBochner space – Type of topological space Measurable function – Function...
actually a total derivative, since the use of Bochner spaces removes the space-dependence.) BochnerintegralBochner measurable function Vector measure Vector-valued...
the change of variables theorem for multiple Bochnerintegrals and Fubini's theorem for Bochnerintegrals using Daniell integration. The book by Asplund...
approach, obtaining the Bochnerintegral. Cauchy principal value – Method for assigning values to certain improper integrals which would otherwise be...
{\displaystyle B} is separable. Bochner measurable function BochnerintegralBochner space – Type of topological space Pettis integral Vector measure Pettis, B...
viewed as a discrete analogue of Lyapunov's theorem. Bochner measurable function BochnerintegralBochner space – Type of topological space Complex measure –...
assumptions. Cf. Bochnerintegral For a continuous function g defined in an open neighborhood of Γ and taking values in L(X), the contour integral ∫Γg is defined...
(abstract) nonhomogeneous Cauchy problem. The integral on the right-hand side as to be intended as a Bochnerintegral. The problem of finding a solution to the...
\qquad h\in H.} This formulation is the Pettis integral but the mean can also be defined as Bochnerintegral μ = E X {\displaystyle \mu =\mathbb {E} X} ...
a Banach space (or Fréchet space), strong measurability usually means Bochner measurability. However, if the values of f lie in the space L ( X , Y )...
physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that...
1977, p. 92. Morgan 1975, p. 3. Stockhausen and Frisius 1998, p. 451. Bochner 1967. Gerstner 1964. Guderian 1985. Sykora 1983. Bandur 2001, p. 54. Cott...
In mathematics, singular integral operators of convolution type are the singular integral operators that arise on Rn and Tn through convolution by distributions;...
generalization of the Fourier integral, "beginning with Plancherel's pathbreaking L2-theory (1910), continuing with Wiener's and Bochner's works (around 1930) and...
(2015). "A generalization of Bochner's formula". Kanemitsu, S.; Tanigawa, Y.; Tsukada, H. (2004). "A generalization of Bochner's formula". Hardy-Ramanujan...
non-equivalent definitions of measurability, such as weak measurability and Bochner measurability, exist. Random variables are by definition measurable functions...
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