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The Hausdorff-integral on h-measure spaces and its applications

Attila Losonczi

Abstract

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 values in $[0,+\infty)\times[0,+\infty)$. In all our intentions, we follow the same attitude that we had in our previous investigation, i.e. we work in the realm of Hausdorff dimension and measure.

The Hausdorff-integral on h-measure spaces and its applications

Abstract

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 values in . In all our intentions, we follow the same attitude that we had in our previous investigation, i.e. we work in the realm of Hausdorff dimension and measure.
Paper Structure (8 sections, 51 equations)

This paper contains 8 sections, 51 equations.

Table of Contents

  1. Introduction
  2. Basic notions and notations
  3. Basic definitions from lahi and lahi2
  4. Generalized integral
  5. Multiplication on $[0,+\infty)\times[-\infty,+\infty]$
  6. Measurability
  7. The integral of functions taking values in ${[0,+\infty)\times[0,+\infty)}$
  8. Applications

Theorems & Definitions (21)

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  • ...and 11 more