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SUMMARY:Paradoxical Decompositions and Colouring Rules
DTSTART:20240613T141500Z
DTEND:20240613T151500Z
DTSTAMP:20240813T224500Z
UID:indico-event-778@events.gwdg.de
DESCRIPTION:Speakers: Robert Simon\n\nA colouring rule is a way to colour
the points x of a probability space according to the colours of finitely m
any measures preserving tranformations of x. The rule is paradoxical if th
e rule can be satisfied a.e. by some colourings\, but by none whose invers
e images are measurable with respect to any finitely additive extension fo
r which the transformations remain measure preserving. We demonstrate para
doxical colouring rules defined via u.s.c. convex valued correspondences (
if the colours b and c are acceptable by the rule than so are all convex c
ombinations of b and c). This connects measure theoretic paradoxes to prob
lems of optimization and shows that there is a continuous mapping from bou
nded group-invariant measurable functions to itself that doesn't have a fi
xed point (but does has a fixed point in non-measurable functions).\nThis
is the solution to the question posed in my 2003 Habilitation talk in Goet
tingen.\n\nhttps://events.gwdg.de/event/778/
LOCATION:Sitzungszimmer (MI)
URL:https://events.gwdg.de/event/778/
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