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Last update: T_KPMS (22.05.2008)
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Last update: T_KPMS (22.05.2008)
To explain foundations of the geometrical measure theory. |
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Last update: T_KPMS (22.05.2008)
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)
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Last update: G_M (29.05.2008)
Lecture. |
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Last update: T_MUUK (19.05.2003)
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. |