RESEARCH IN PAIRS  RECHERCHE EN BINOMES
gMeasures: Uniqueness and Properties (event 2112) gmesures : unicité et propriétés Dates: tbc Place: CIRM (Marseille Luminy, France) 
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Background
An interesting problem in probability theory was introduced by Keane in 1972 and formulated in terms of what he called gmeasures. Their definition can be formulated in terms of the jacobian (which is function and denoted by the g in question) of the measure and the requirement that it is continuous. A basic problem is to determine what stronger properties of the jacobian are required to show that there is associated a unique gmeasure. A particularly fruitful approach is using transfer operators. A major breakthrough some years ago was when Oberg and Johansson used a martingale argument to give a criterion for uniqueness. Since then, there has been steady progress in obtaining optimal hypotheses for uniqueness of the gmeasure. Aims We would like to explore the delicate question of the threshold conditions for the uniqueness of the gmeasures. This is expressed in terms of the regularity of the function g, usually expressed in terms of the variations of the function. Pollicott, Johansson (Gavle) and Oberg (Uppsala) have a longstanding collaboration on this project which has already resulted in substantial progress. 

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