A variation on a theorem by Fremlin for doubling Radon measures

10 November 2023
Start time 
10:00 am
PovoZero - Via Sommarive 14, Povo (Trento)
Seminar Room 1 - Department of Mathematics
Target audience: 
University community
Contact person: 
Prof. Andrea Marchese
Contact details:

Cesare Straffelini
PhD Student in Mathematics

We will start by proving a theorem by Fremlin: by assuming a fragment of Martin’s Axiom, in particular Martin’s Axiom for partial order with the Knaster property, then every Radon measure on a locally compact separable metric space is continuum-additive on measurable sets. Afterwards, we will prove a variation of this result: if the measure is doubling, then a weaker fragment of Martin’s Axiom is needed: indeed, Martin’s Axiom for sigma-linked partial orders is enough.

The seminar corresponds to the final exam of “Geometric Measure Theory"