Bochner integral


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Bochner integral

[¦bäk·nər int·i·grəl]
(mathematics)
The Bochner integral of a function, ƒ, with suitable properties, from a measurable set, A, to a Barach space, B, is the limit of the integrals over A of a sequence of simple functions, sn, from A to B such that the limit of the integral over A of the norm of ƒ -sn approaches zero.
References in periodicals archive ?
A measurable function x : J [right arrow] X is Bochnerintegrable ifand only if [parallel]x[parallel] is Lebegue integrable (For properties of the Bochner integral see Yosida [26]).
Some Gruss type inequalities for the Bochner integral of vector-valued functions in real or complex Banach spaces are given.
Keywords and Phrases: Gruss inequality, Bochner integral, Banach spaces, Hilbert spaces.
The following Sonin type identity for the Bochner integral holds: