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2 = Geometric measure theory, fall 2014 =
3
4 === Lecturer ===
5
6 [[Pertti Mattila>>doc:mathstatHenkilokunta.Mattila, Pertti]]
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8 === Scope ===
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10 10 sp.
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12 === Type ===
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14 Advanced studies
15
16 === Prerequisites ===
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18 Basic knowledge of measure and integration theory such as the courses "Mitta ja integraali" and "Reaalianalyysi I". "Reaalianalyysi II" is useful but not necessary.
19
20 === Lectures ===
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22 Weeks 36-42 and 44-50, Wednesday 14-16 in room B322 and Thursday 14-16 in room C122.
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24 The first lecture is on Wednesday, September 3. On Thursday, September 4, there will be no lecture.
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26 **The last two weeks:**
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28 Lectures normally on December 3 and 4.
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30 Thursday, December 4, 16-18, CK111: Joni Teräväinen: Marstrand's projection theorem
31
32 **Change of day:**
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34 Thursday (not Wednesday), December 11, 14-16, B322: Laura Venieri: Besicovitch sets
35
36 === Course description ===
37
38 Geometric measure is an area of mathematics where measure theoretic methods are used to study geometric properties of many different kinds of objects. These include generalized surfaces (rectifiable sets, currents, varifolds) and fractals. The field has applications and connections to many branches of mathematics, for example, calculus of variations, partial differential equations, real, complex and harmonic analysis, dynamical systems and probability theory. The topics discussed will include
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40 isoperimetric and isodiametric inequalities,
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42 area and coarea (change of variable) formulas
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44 rectifiable sets and measures
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46 sets of finite perimeter
47
48 === [[Lecture notes>>attach:gmt.pdf]] ===
49
50 === Exams ===
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52
53
54 === Bibliography ===
55
56 L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, 1992.
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58 H. Federer, Geometric Measure Theory, Springer-Verlag, 1969.
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60 P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, 1995.
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62 F.H. Lin and X. Yang, Geometric Measure Theory, International Press, 2002.
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64 F. Morgan, Geometric Measure Theory, A Beginner's Guide, Academic Press, 1988.
65
66 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57266||shape="rect"]] ===
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68
69 Did you forget to register? [[ What to do?>>doc:mathstatOpiskelu.Kysymys4]]
70
71 === Exercises ===
72
73 Exercise sessions on Thursdays 16-18 in CK111. The first will be on September 18.
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75 [[Exercise 1>>attach:gmt-ex1.pdf]]
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77 [[Exercise 2>>attach:gmt-ex2.pdf]]
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79 [[Exercise 3>>attach:gmt-ex3.pdf]]
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81 [[Exercise 4>>attach:gmt-ex4.pdf]]
82
83 [[Exercise 5>>attach:gmt-ex5.pdf]]
84
85 [[Exercise 6>>attach:gmt-ex6.pdf]]
86
87 [[Exercise 7>>attach:gmt-ex7.pdf]]
88
89 [[Exercise 8>>attach:gmt_ex8.pdf]]
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100 Teacher
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105 Thursday
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111 Pertti Mattila
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