Abstract: In this paper, a class of approximate interpolation neural networks is constructed to approximate Lebesgue integrable functions. It is showed that the networks can arbitrarily approximate ...

The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function ; that is, for ...

Using functions of bounded variation, we define a Volterra type derivative of the linear functional associated with a Lebesgue integrable function and show that it is equal to this function almost ...

ABSTRACT: In this study, we prove the of existence of solutions of a convolution Volterra integral equation in the space of the Lebesgue integrable function on the set of positive real numbers and ...

A PDF has to be non-negative, Lebesgue-integrable, and normalized to an integral of unity over the whole space. Although it is far from mathematically rigorous, the following rationale suggests that a ...

This file proves the Fundamental Theorem of Calculus and integration-by-parts for absolutely continuous functions. Since there is no API for absolutely continuity in Mathlib at the moment, I am using ...

Let X be a weakly $Lindel\ddot{o}f$ determined Banach space. We prove that if X is non-separable, then there exist a complete probability space (Ω, Σ, μ) and a ...