# Operators on Spaces of Functions and Measures. Vector Invariant (Fractal) Measures

## TL;DR

This paper develops a general framework for operators on function and measure spaces, introducing integral operators that generalize Markov operators to produce vector invariant (fractal) measures, with concrete examples.

## Contribution

It introduces a unified schema for operators on functions and measures, generalizing Markov operators to vector invariant measures using contractions.

## Key findings

- Generalized Markov operators to vector measures
- Established conditions for vector invariant (fractal) measures
- Provided concrete examples illustrating the theory

## Abstract

We consider a general schema involving measure spaces, contractions and linear and continuous operators. Within the framework of this schema we use our sesquilinear uniform integral and introduce some integral operators on continuous vector functions spaces, which lead us to operators on spaces of vector measures. Using these last operators, we generalize the Markov operators, obtaining via contractions vector invariant (fractal) measures. Concrete examples are provided.