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Selected results completing the lecture NMMA203 Measure and Integration Theory, with respect to applications in
probability theory> Hausdorff measure and dimension, Lebesgue density theorem, Haar measure, disintegration
theorem.
Last update: T_MUUK (27.04.2016)
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To teach the students of the master studies in Probability, Mathematical Statistics and Econometrics certain approaches useful in probability theory Last update: T_MUUK (27.04.2016)
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Ústní zkouška. Last update: Zichová Jitka, RNDr., Dr. (14.06.2019)
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Morgan F.: Geometric Measure Theory: a Beginner's Guide.Academic Press, San Diego 1988 Mattila P.: Geometry of Sets and Measures in Euclidean Spaces. Cambridge Univ. Press, Cambridge 1995 Krantz S.G., Parks H.R.: Geometric Integration Theory. Birkhäuser, Boston 2008 Last update: T_MUUK (27.04.2016)
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Lecture. Last update: G_M (16.05.2013)
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Zkouška probíhá ústní formou. Její součástí je prezentace vyřešeného předem zadaného cvičení a zodpovězení otázek týkajících se odpřednesené látky. Last update: Rataj Jan, prof. RNDr., CSc. (12.10.2018)
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1. k-dimensional Hausdorff measure, Hausdorff dimension, covering theorems, Lebesgue density theorem. 2. Invariant measures on a compact topological group, Haar measure, integral-geometric measure. 3. Disintegration theorem for measures on Cartesian products, existence of regular versions of conditional probabilities, random measure. Last update: T_MUUK (27.04.2016)
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Basic cousres of mathematical analysis and measure and integration theory. Last update: Rataj Jan, prof. RNDr., CSc. (15.06.2021)
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