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Hausdorff measure in $R^d$, Hausdorff dimension, approximate limit, density of
sets, lipschitz mappings and differentiability, area and co-area formulae,
Hausdorff rectifiable sets, approximate tangent cone, integration of
differential forms, currents.
Last update: T_MUUK (14.05.2013)
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To explain foundations of the geometrical measure theory. Last update: T_MUUK (14.05.2013)
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Literature: (1) H. Federer: Geometric Measure Theory (Springer, 1969) (2) P. Mattila: Geometry of Sets and Measures in Euclidean Spaces (Cambridge, 1995) (3) F. Morgan: Geometric Measure Theory: A Beginner's Guide (Acad. Press, 1988)
Last update: T_MUUK (14.05.2013)
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Lecture. Last update: T_MUUK (14.05.2013)
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1. k-dimensional measures in Rd: Hausdorff measure, integral-geometric measure, Minkowski content. 2. k-dimensional density of a set in a point, approximative limit, approximative continuity, approximation of lipschitz mappings by differentiable mappings. 3. k-dimensional Jacobian, substitution theorems: area and coarea formulae. 4. tangent cone, approximative tangent cone, Hausdorff rectifiable sets, area and coarea theorem for lipschitz mappings an Hausdorff rectifiable sets. 5. k-vectors and k-covectors, outer multiplication, differential forms and currents. Last update: T_MUUK (14.05.2013)
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