A note on iterated function systems with discontinuous probabilities

We consider an example of an iterated function system with discontinuous probabilities. We prove that it posses an invariant probability measure. We also prove that it is asymptotically stable provided probabilities are positive.

► Certain iterated function system with discontinuous probabilities is discussed.
► Existence of an invariant measure via the Schauder–Tychonov theorem is established.
► Asymptotic stability of the system under examination is proved.