2010/09/01 by Larson, Paul B.
#03E35 #28A20 #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO)
paper · doi:10.48550/arxiv.1009.0065
The Filter Dichotomy says that every uniform nonmeager filter on the integers is mapped by a finite-to-one function to an ultrafilter. The consistency of this principle was proved by Blass and Laflamme. A function between topological spaces is universally measurable if the preimage of %every open subset of the codomain is measured by every Borel measure on the domain. A medial limit is a universally measurable function from P(ω) to the unit interval [0,1] which is finitely additive for disjoint sets, and maps singletons to 0and ω to 1. Christensen and Mokobodzki independently showed that the Continuum Hypothesis implies the existence of medial limits. We show that the Filter Dichotomy implies that there are no medial limits.