Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Hausdorff-integral and its applications

Attila Losonczi

Abstract

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 its similarities to the properties of the Lebesgue integral. We present many applications as well.

The Hausdorff-integral and its applications

Abstract

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 its similarities to the properties of the Lebesgue integral. We present many applications as well.
Paper Structure (9 sections, 48 equations)

This paper contains 9 sections, 48 equations.

Table of Contents

  1. Introduction
  2. Basic notions and notations
  3. The bases of the integral
  4. Structures on $[0,+\infty)\times[-\infty,+\infty]$ and its subsets
  5. Sequences and series on $[0,1]\times[-\infty,+\infty]$
  6. Basic definitions and results
  7. Integrals of series
  8. Applications
  9. Applications for deficiency measurement

Theorems & Definitions (22)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • ...and 12 more