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The basic properties of the Daniell integral are presented. We do not use the standard approach of introducing auxiliary spaces of the over-functions and under-functions. Instead, we use a simple and direct approach based on approximating integrable functions by absolutely convergent series of simple functions.
In this article we discuss a relation between the string topology and differential forms based on the theory of Chens iterated integrals and the cyclic bar complex.
The theory of integration over R is rich with techniques as well as necessary and sufficient conditions under which integration can be performed. Of the many different types of integrals that have been developed since the days of Newton and Leibniz,
Given a two-variable function f without critical points and a compact region R bounded by two level curves of f, this note proves that the integral over R of fs second-order directional derivative in the tangential directions of the interceding level
This note concerns the general formulation by Preiss and Uher of Kestelmans influential result pertaining the change of variable, or substitution, formula for the Riemann integral.
In this paper, we prove a new integral representation for the Bessel function of the first kind $J_mu(z)$, which holds for any $mu,zinmathbb{C}$.