A characterisation of absolutely continuous measures on topological semigroups

Absolutely Continuous Invariant Measures That Are Maximal

Let A be a certain irreducible 0-1 matrix and let t denote the family of piecewise linear Markov maps on [0,1] which are consistent with A. The main result of this paper characterizes those maps in t whose (unique) absolutely continuous invariant measure is maximal, and proves that for "most" of the maps that are consistent with A, the absolutely continuous invariant measure is not maximal.

Continuous Bounded Cohomology of Topological Semigroups

We define a cohomology theory for topological semigroups, with seminormed cohomology groups. Our theory can be considered as a topological version of bounded cohomology of discrete semigroups. 1. Definition of the cohomology Bounded cohomology was first defined for discrete groups by F. Trauber and then for topological spaces by M. Gromov [6]. In this paper we establish a topological bounded co...

On Absolutely Continuous Transformations

Convergence on Manifolds of Gibbs Measures Which Are Absolutely Continuous with Respect to Hausdorff Measures

We identify a sufficiant condition for a sequence of Gibbs measures Pλ with the density Zλe01, v ∈ Rn, defined on a state space of v′s, to converge weakly in a sense of measures to a Gibbs measure with a density Zλe −J0(v), where the dominating measure for the density is the Hausdorff measure with an appropriate dimension. The function J0 identifies an objective and J1 defines a constraint. The...

The Existence of Absolutely Continuous Local Martingale Measures

We investigate the existence of an absolutely continuous martingale measure. For continuous processes we show that the absence of arbitrage for general admissible integrands implies the existence of an absolutely continuous (not necessarily equivalent) local martingale measure. We also rephrase Radon-Nikodym theorems for predictable processes. 1.Introduction. In our paper Delbaen and Schacherma...