Seminar

# 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

Attendance:

Free

Contact person:

Prof. Andrea Marchese

Contact details:

phd.maths@unitn.it

**Cesare Straffelini**

PhD Student in Mathematics

**Abstract**:

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"**

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