Kurssi: MS-E1281 - Real Analysis D, Lecture, 26.2.2024-12.4.2024

Welcome to the home page of a course in advanced real analysis. The course practices will be discussed in the first lecture on Mon 26 February 2024 at 10-12 in M3. The lectures are on Mondays in M234 (M3) and on Thursdays in M140. We have adopted a flipped classroom model for the course. The participants are expected to study the announced pages of the lecture notes before each lecture.

Prerequisites: MS-E1280 Measure and Integral.

Grading: There is no final exam. The grading is based on homework assignments and attendance.

Solved homework assignments Grade

90% 5

80% 4

70% 3

60% 2

50% 1

Instructor: Juha Kinnunen

Assistant: Kim Myyryläinen

Schedule

Mon 26 Feb: Pages 1-11 of the lecture notes.

Thu 29 Feb: Pages 12-20 of the lecture notes.

Mon 4 March: Pages 21-32 of the lecture notes.

Thu 7 March: Pages 33-43 of the lecture notes.

Mon 11 March: Pages 44-55 of the lecture notes. Section 2.6 (pages 56-59) contains additional material for those who are interested in Sobolev spaces.

Thu 14 March: Pages 60-73 of the lecture notes.

Mon 18 March: Pages 74-88 of the lecture notes.

Thu 21 March: Pages 89-103 of the lecture notes. The proof of the Besicovitch covering theorem on pages 92-96 is somewhat technical and can be omitted in the first reading.

Mon 25 March: Pages 104-114 of the lecture notes.

Thu 28 March: No lecture.

Mon 1 April: No lecture.

Thu 4 April: No lecture.

Mon 8 April: Pages 115-134 of the lecture notes. The proof of the Riesz representation theorem for Radon measures (Theorem 5.6) on pages 128-133 can be omitted in the first reading.

Thu 11 April: Pages 135-149 of the lecture notes. The proof of Mazur's lemma (Theorem 5.31) on pages 146-147 can be omitted in the first reading.

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MS-E1281 - Real Analysis D, Lecture, 26.2.2024-12.4.2024

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