We prove that all negative generalized Boole transformations are conservative, exact, pointwise dual ergodic, and quasi-finite with respect to Lebesgue measure on the real line. We then provide a formula for computing the Krengel, Parry, and Poisson entropy of all conservative rational functions that preserve Lebesgue measure on the real line.
"Ergodic Properties of Rational Functions that Preserve Lebesgue Measure on ℝ." Real Anal. Exchange 43 (1) 137 - 154, 2018. https://doi.org/10.14321/realanalexch.43.1.0137