Analysis seminar: Irina Markina
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Speaker: Irina Markina, Professor, Mathematical Department, UiB
Title: Hausdorff measure.
Abstract: We will introduce the general construction of Caratheodory of the outer measure and shows that it is Borel regular measure on Borel sets. The particular case of that construction is the Hausdorff measure in an arbitrary metric space. We compare the Hausdorff measure with the Lebesgue measure in the Euclidean space and introduce the Hausdorff dimension of a set. As an application we calculate the dimension of the Koch snowflake.
Title: Hausdorff measure.
Abstract: We will introduce the general construction of Caratheodory of the outer measure and shows that it is Borel regular measure on Borel sets. The particular case of that construction is the Hausdorff measure in an arbitrary metric space. We compare the Hausdorff measure with the Lebesgue measure in the Euclidean space and introduce the Hausdorff dimension of a set. As an application we calculate the dimension of the Koch snowflake.
23.09.2014