Generalized Hausdorff Integral and Its Applications: Applications

Table of Links

Abstract and 1 Introduction

1.1 Basic notions and notations

1.2 Basic definitions from [7] and [8]

2 Generalized integral

2.1 Multiplication on [0, +∞) × [−∞, +∞]

2.2 Measurability

2.3 The integral of functions taking values in [0, +∞) × [0, +∞)

3 Applications

4 References

3 Applications

We provide three applications that are sophisticated deficiency measurements for continuity, lineness and convexity (for basic notions and notations see [9] and [7] subsection 3.1). Here we will just define the deficiency measurements with a little explanation, and we will not add reasonable statements as our purpose is not that currently.

Let f : R → R be a function. We want to measure how much f is not continuous. Set