相关论文: Notes on Lebesgue integration

We explore the properties of an interesting new example of a function which is Lebesgue integrable but not Riemann integrable.

New cases of the multiplicity conjecture are considered.

We present a replacement for traditional Riemann integrals in undergraduate calculus, which supplements naive precalculus and at the same time opens a way to more sophisticated theories such as Lebesgue integration.

We present a simple iteration for the Lebesgue identity on partitions, which leads to a refinement involving the alternating sums of partitions.

This text grew out of notes I have used in teaching a one quarter course on integration at the advanced undergraduate level. My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to…

We present a new type of integral that is supposed to extend the usability of the Lebesgue integral in certain types of investigations. It is based on the Hausdorff dimension and measure. We examine the basic properties of the integral and…

Leonida Tonelli devised an interesting and efficient method to introduce the Lebesgue integral. The details of this method can only be found in the original Tonelli paper and in an old italian course and solely for the case of the functions…

We present a modification of Riesz's construction of the Lebesgue integral, leading directly to finite or infinite integrals, at the same time simplifying the proofs.

Discrete analogs of the Lebedev transforms with the product of the modified Bessel functions are introduced and investigated. Several expansions of suitable functions and sequences in terms of the series and integrals, involving the…

Work in progress concerning alternative formalizations of arithmetic.

This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function…

We present in this survey some results regarding Riemann_Lebesgue integrability with respect to arbitrary non-additive set functions.

The paper suggests a slightly more rigorous justification to Wang et al.'s work from 2007, and introduces the Slanted Line Integral.

We deduce mixed quasi-norm estimates of Lebesgue types on semi-continuous convolutions between sequences and functions which may be periodic or possess a weaker form of periodicity in certain directions. In these directions, the Lebesgue…

Two new approaches to numerical QFT are presented.

The present article is devoted to one example which related to the Salem function. The main attention is given to properties of one type of functions including items related to functional equations, graphs, the Lebesgue integral, etc.

A proposed solution to the Riemann Hypothesis

A proposed modification of the dinamic subgrid scale closure method for LES.

Lebesgue's dominated convergence theorem is a crucial pillar of modern analysis, but there are certain areas of the subject where this theorem is deficient. Deeper criteria for convergence of integrals are described in this article.

We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.