University of Jyväskylä

Dissertation: 12.12 Thin and Fat sets: geometry of doubling measures in metric spaces (Ojala)

Start date: Dec 12, 2014 12:00 AM

End date: Dec 12, 2014 03:00 PM

Location: Seminaarinmäki, Seminarium, S212

Tuomo Ojala.M.Sc. Tuomo Ojala defends his doctoral dissertation in Mathematics. Opponent Associate Professor Tuomas Hytönen (University of Helsingi) and custos Adjunct Professor Tapio Rajala (University of Jyväskylä). The event is in Finnish.


The area of the thesis is geometric measure theory. We study doubling measures in metric spaces. Measure is called doubling if a measure of a ball controls the measure of the ball with doubled radius. A subset of a space is called thin if it has zero measure with respect to all doubling measures and fat if it has positive measure for all doubling measures. As main results we give characterizations of thinness or fatness according to a construction parameter of certain cut-out sets. We also give conditions that guarantee that the doubling property of a measure is preserved when the measure is restricted to a subset of the space. Finally we give an example of a continuous function whose graph has positive doubling measure.

The dissertation is published in the series University of Jyväskylä, Department of Mathematics and Statistics, Report nro. 144, Jyväskylä 2014, ISBN 978-951-39-5947-0, ISSN 1457-8905. The publication can be inquired from Tuomo Ojala.

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