A Young-type integration on self-similar sets in intervals

TL;DR

This paper generalizes Young integration to self-similar sets within intervals, establishing conditions for integrability and demonstrating key properties like substitution and parts integration.

Contribution

It introduces a new integration framework for self-similar sets, extending classical Young integration with proven properties and practical examples.

Findings

Established a sufficient condition for integrability on self-similar sets.

Proved fundamental properties such as substitution, parts, and term-by-term integration.

Provided examples illustrating the properties and applicability of the generalized integration.

Abstract

We introduce a generalization of the Young integration on self-similar sets defined in a closed interval and give a sufficient condition of its integrability. We also prove integration by substitution, integration by parts and term-by-term integration and give examples of the properties.