Absolutely Continuous Invariant Measures
Abraham Boyarsky, Paweł Góra · Birkhäuser Boston eBooks · 1997
In this chapter, we prove the existence of absolutely continuous invariant measures (acim) using bounded variation techniques. Examples of transformations having an acim were known to Ulam and von Neumann [Ulam and von Neumann, 1940]. Rényi [Rényi, 1957] was the first one to define a class of transformations that have an acim. His key idea of using distortion estimates has been used in more general proofs [Adler and Flatto, 1991].