Related papers: L-valued integration

Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars $\mathbb{R}$ or $\mathbb{C}$ by a real or complex Dedekind complete unital…

In this article, we introduce the notion of a curved absolute $\mathcal{L}_\infty$-algebra, a structure that behaves like a curved $\mathcal{L}_\infty$-algebra where all infinite sums of operations are well-defined by definition. We develop…

In this paper we develop a theory of integration for locally band preserving functions, introduced by Ercan and Wickstead, on Dedekind complete $f$-algebras. Specifically, we construct Darboux and Riemann integrals and show that they are…

In this paper, we introduce and study the Fourier transform of functions which are integrable with respect to a vector measure on a compact group (not necessarily abelian). We also study the Fourier transform of vector measures. We also…

This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…

We identify simple universal properties that uniquely characterize the Lebesgue $L^p$ spaces. There are two main theorems. The first states that the Banach space $L^p[0, 1]$, equipped with a small amount of extra structure, is initial as…

We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…

The article presents a new method of integration of functions with values in Banach spaces. This integral and related notions prove to be a useful tool in the study of Banach space geomtry.

In this paper, we introduce and study the Weyl transform of functions which are integrable with respect to a vector measure on a phase space associated to a locally compact abelian group. We also study the Weyl transform of vector measures.…

We introduce first weighted function spaces on Rd using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on…

This paper studies absolute integrability for functions with values in semi- normed spaces and in locally convex topological vector spaces (LCTVS). We introduce an \emph{upper-integral} approach (based on a $\rho$-variational measure…

We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of…

We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving in particular a detailed study of Gauss and Jacobi sums),…

We are going to widen the scope of the previously defined Hausdorff-integral in two ways. First, in the sense, that we develop the theory of the integral on some naturally generalized measure spaces. Second, we extend it to functions taking…

Integration, just as much as differentiation, is a fundamental calculus tool that is widely used in many scientific domains. Formalizing the mathematical concept of integration and the associated results in a formal proof assistant helps in…

Let A be the integral closure of the ring of polynomials CC[t], within the field of algebraic functions in one variable. We show that A interprets the ring of integers. This contrasts with the analogue for finite fields, proved to have a…

We present closed forms for several functions that are fundamental in number theory and we explain the method used to obtain them. Concretely, we find formulas for the p-adic valuation, the number-of-divisors function, the sum-of-divisors…

We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an $L^{p}$ Liouville type theorem which is a quantitative integral $L^{p}$ estimate of harmonic functions analogous to Karp's…

We define a p-norm in the context of quantum random variables, measurable operator-valued functions with respect to a positive operator-valued measure. This norm leads to a operator-valued L^p space that is shown to be complete. Various…

In this paper we consider generalized square function norms of holomorphic functions with values in a Banach space. One of the main results is a characterization of embeddings of the form \[L^p(X)\subseteq \gamma(X) \subseteq L^q(X),\] in…