A variation on a theorem by Fremlin for doubling Radon measures
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"