[Settfa] Tuesday 18/04, Janusz Morawiec

[kubis at math.cas.cz]

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 Tuesday 18th April, 10:00am 
 
  Place: IM in konírna 

 
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 Speaker:Janusz Morawiec,  University of Silesia in Katowice, Poland
 Title: Invariant measures for uncountable random interval homeomorphisms

 Abstract  

 Fix a probability space (?,A,P) and a function f:[0,1]x??[0,1] such that for every x?[0,1], the function f(x,•) is A-measurable, and for every ???, the function f(•,?) is an increasing homeomorphism of [0,1] onto itself. Assume that for any x? (0,1) there exists a set B?A such that P(B)>0 and f(x,?)<x for every ??B, or for any x? (0,1) there exists a set C?A such that P(C)>0 and f(x,?)>x for every ??C. We give a necessary and sufficient condition for the iterated function system with probabilities ({f(•,?),???},P) to have exactly one invariant measure m with m((0,1))=1. We also investigate the properties of this iterated function system with probabilities.
 
Joint work with Tomasz Szarek.

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .