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The lecture is focused on fundamental principles in analysis which are of great importance for applications in stochastic and financial mathematics.

The main topics are:

• Foundations of mathematical analysis
• Measure and integration
• Hilbert spaces
• Fourier transform and characteristic functions

In the lecture we will also revisit the fundamental material from the introductory course An Introduction to Measure Theoretic Probability. The former lecture notes by Markus Kunze can be found on the course website Applied Analysis in WS 2011/2012.

The lecture notes of this year's course will be made available in digital form. Feedback and corrections are very much appreciated! Currently availlable:
Chapter II: Normed Spaces (last update 2014-11-12)
Chapter III: Measure Theory, Part 1 (last update 2014-12-19)
Chapter III: Measure Theory, Part 2 (last update 2015-01-17)
Chapter III: Measure Theory, Part 3 (last update 2015-02-05)
Chapter IV: Hilbert spaces (last update 2015-02-06)

The following books can be found in the course reserve collection in the He18 library.

• Bartle: The elements of integration and Lebesgue measure
• Conway: A course in functional analysis
• Jost: Postmodern analysis
• Lang: Undergraduate analysis
• Varadhan: Probability theory
• Stein and Shakarchi: Real analysis – measure theory, integration, and Hilbert spaces

The first exam is a 2 hour written exam that will take place on 18 Feburary 2015 (Updated!) in He18 E.120 from 10 a.m. to noon. In order to take the exam, you have to register on time via LSF-QISPOS.

Only participants of the first exam who did not pass will be admitted to the second exam. If a second exam is required, it likely will be scheduled for the first lecture week of the summer semester. Depending on the participants' preference, we will decide whether the second exam is a written or an oral exam.

Dates and locations.

Lectures

• Thursday, 16–18 (N24/254)
• Friday, 8–10 (He18, E.60)

Exercises 

• Friday, 14–16 (He18, E.20)

SheetDiscussion

Sheet01.pdf Solution01.pdf Sheet02.pdf Sheet03.pdf Sheet04.pdf Sheet05.pdf Sheet06.pdf Sheet07.pdf Sheet08.pdf Sheet09.pdf Sheet10.pdf Sheet11.pdf Sheet12.pdf MockExam.pdf	2014-10-24 2014-10-31 2014-11-7 2014-11-14 2014-11-21 2014-11-28 2014-12-5 2014-12-12 2014-12-19 2015-01-16 2015-01-23 2015-01-30 2015-02-13