In mathematics, Bochner spaces are a generalization of the concept of spaces to functions whose values lie in a Banach space which is not necessarily the space or of real or complex numbers.
The space consists of (equivalence classes of) all Bochner measurable functions with values in the Banach space whose norm lies in the standard space. Thus, if is the set of complex numbers, it is the standard Lebesgue space.
Almost all standard results on spaces do hold on Bochner spaces too; in particular, the Bochner spaces are Banach spaces for
Bochner spaces are named for the mathematician Salomon Bochner.
mathematics, Bochnerspaces are a generalization of the concept of L p {\displaystyle L^{p}} spaces to functions whose values lie in a Banach space which is...
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...
the spaces of Bochner and Pettis integral functions mentioned earlier; in short, they are indistinguishable. Bochnerspace – Type of topological space Orlicz...
mathematics – specifically, in functional analysis – a Bochner-measurable function taking values in a Banach space is a function that equals almost everywhere the...
Salomon Bochner (20 August 1899 – 2 May 1982) was a Galician-born mathematician, known for work in mathematical analysis, probability theory and differential...
vector spaces in abstract mathematics, by Wikipedia page. Banach space Besov spaceBochnerspace Dual space Euclidean space Fock space Fréchet space Hardy...
infinite-dimensional vector space, other non-equivalent definitions of measurability, such as weak measurability and Bochner measurability, exist. Random...
characteristic functional on a nuclear space A , {\displaystyle A,} the Bochner–Minlos theorem (after Salomon Bochner and Robert Adol'fovich Minlos) guarantees...
{\displaystyle Y} and L 1 ( [ 0 , 1 ] , Y ) {\displaystyle L^{1}([0,1],Y)} the space of Bochner-measurable and integrable functions from [ 0 , 1 ] {\displaystyle [0...
{\displaystyle B} is separable. Bochner measurable function Bochner integral Bochnerspace – Type of topological space Pettis integral Vector measure Pettis...
are necessary.[citation needed] Bochner measurable function Bochner integral Bochnerspace – Type of topological space Vector measure Weakly measurable...
analogue of Lyapunov's theorem. Bochner measurable function Bochner integral Bochnerspace – Type of topological space Complex measure – Measure with complex...
Salomon Bochner. The subject was eventually systematically developed in the early 1950s by Nachman Aronszajn and Stefan Bergman. These spaces have wide...
in 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 )...
onto M. There is a connection between Bochnerspaces and Banach bundles. Consider, for example, the Bochnerspace X = L²([0, T]; H1(Ω)), which might arise...
using other norms by Besicovitch, Stepanov, Weyl, von Neumann, Turing, Bochner and others in the 1920s and 1930s. Bohr (1925) defined the uniformly almost-periodic...
manifold has positive Ricci curvature then its fundamental group is finite. Bochner's formula. If a compact Riemannian n-manifold has non-negative Ricci curvature...
Amanda Babs Olusanmokun as Damian Celestino Cornielle as Celestino Hart Bochner as Lieutenant Carlotta Montanari as Magdalena George Payne Chris Coppola...
building and Posner Hall. The Campo was designed and created by artist Mel Bochner and landscape architect Michael Van Valkenburgh. The Campo consists of...
the tensor Laplacian. This, for instance, explains its presence in the Bochner formula, which is used ubiquitously in Riemannian geometry. For example...
The Bochner integral, an extension of the Lebesgue integral to a more general class of functions, namely, those with a domain that is a Banach space. The...
(L1 distance, ReLU activation, arbitrary depth, minimal width) — For any Bochner–Lebesgue p-integrable function f : R n → R m {\displaystyle f:\mathbb {R}...
Global Information
