## Institute for Mathematical Sciences

## Preprint ims92-1

** M. Martens**
* The Existence of Sigma-Finite Invariant Measures, Applications to Real One-Dimensional Dynamics.*

Abstract: A general construction for $\sigma-$finite absolutely continuous invariant measure will be presented. It will be
shown that the local bounded distortion of the Radon-Nykodym
derivatives of $f^n_*(\lambda)$ will imply the existence of a
$\sigma-$finite invariant measure for the map $f$ which is
absolutely continuous with respect to $\lambda$, a measure on
the phase space describing the sets of measure zero.
Furthermore we will discuss sufficient conditions for the
existence of $\sigma-$finite invariant absolutely continuous
measures for real 1-dimensional dynamical systems.

View ims92-1 (PDF format)