BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Georg Lehner (University of Münster) DTSTART:20251021T150000Z DTEND:20251021T163000Z DTSTAMP:20260422T174255Z UID:tandg/34 DESCRIPTION:Title: M easure theory via locales\nby Georg Lehner (University of Münster) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nThe re are two oftentimes unspoken truths in measure theory. 1) Practically al l useful measures in practice are given by Radon measures. 2) One does not really care so much about the sigma-algebra of measurable sets\, but rath er about its quotient by the ideal of null sets.\n\nThe quotient of measur able sets by null sets is\, in the case of a given Radon measure\, an exam ple of what is called a measurable locale\, and can be treated like a (usu ally point-free) space. We argue that this measurable locale can be constr ucted directly from a Grothendieck topology on the poset of compact sets. This opens the door to a purely sheaf-theoretic perspective on measure the ory. As an application\, we show that the locale of sublocales of a given Hausdorff space X equipped with a Radon measure can be equipped with a nat ural extension of the measure\, invariant under measure preserving homeomo rphisms.\n LOCATION:https://researchseminars.org/talk/tandg/34/ END:VEVENT END:VCALENDAR