Invariant Measure Associated with a Generalized Countable Iterated Function System

Generalized countable iterated function systems (GCIFS) are an extension of countable iterated function systems by considering contractions from X x X into X instead of contractions on the compact metric space X into itself. For a GCIFS endowed with a system of probabilities we associate an invariant and normalized Borel measure whose support is just the attractor of the respective GCIFS, extending the classical Hutchinson's construction.