Displaying similar documents to “On r -dimensional integrals in ( r + 1 ) -space”

Order convergence of vector measures on topological spaces

Surjit Singh Khurana (2008)

Mathematica Bohemica

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Let X be a completely regular Hausdorff space, E a boundedly complete vector lattice, C b ( X ) the space of all, bounded, real-valued continuous functions on X , ℱ the algebra generated by the zero-sets of X , and μ C b ( X ) → E a positive linear map. First we give a new proof that μ extends to a unique, finitely additive measure μ ℱ → E + such that ν is inner regular by zero-sets and outer regular by cozero sets. Then some order-convergence theorems about nets of E + -valued finitely additive measures on ℱ are proved,...

On integration of vector functions with respect to vector measures

José Rodríguez (2006)

Czechoslovak Mathematical Journal

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We study integration of Banach space-valued functions with respect to Banach space-valued measures. We focus our attention on natural extensions to this setting of the Birkhoff and McShane integrals. The corresponding generalization of the Birkhoff integral was first considered by Dobrakov under the name S * -integral. Our main result states that S * -integrability implies McShane integrability in contexts in which the later notion is definable. We also show that a function is measurable and...

A Whitney extension theorem in L p and Besov spaces

Alf Jonsson, Hans Wallin (1978)

Annales de l'institut Fourier

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The classical Whitney extension theorem states that every function in Lip ( β , F ) , F ⊂ R n , F closed, k < β ≤ k + 1 , k a non-negative integer, can be extended to a function in Lip ( β , R n ) . Her Lip ( β , F ) stands for the class of functions which on F have continuous partial derivatives up to order k satisfying certain Lipschitz conditions in the supremum norm. We formulate and prove a similar theorem in the L p -norm. The restrictions to R d , d < n , of the Bessel potential spaces in R n and the Besov or generalized Lipschitz...

Positive vector measures with given marginals

Surjit Singh Khurana (2006)

Czechoslovak Mathematical Journal

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Suppose E is an ordered locally convex space, X 1 and X 2 Hausdorff completely regular spaces and Q a uniformly bounded, convex and closed subset of M t + ( X 1 × X 2 , E ) . For i = 1 , 2 , let μ i ∈ M t + ( X i , E ) . Then, under some topological and order conditions on E , necessary and sufficient conditions are established for the existence of an element in Q , having marginals μ 1 and μ 2 .