Course Catalog 2009-2010 International Basic Pori International Postgraduate Open University |Degrees|     |Study blocks|     |Courses|

Person responsible

Sirkka-Liisa Eriksson

Implementations

	Lecture times and places	Target group recommended to
Implementation 1	Periods 1 1 - 2

Requirements

Written examination

Principles and baselines related to teaching and learning

-

Learning outcomes

Basic skills on measure and integration theory. The course lays down the basis for further special courses on analysis and stochastics. Special attention is paid for logical and elegant presentation of the material.

Content

Content	Core content	Complementary knowledge	Specialist knowledge
1.	Lebesgue outer measure and measure in case of real numbers General measure and integration theory
2.	Absolutely continuity and singularity with respect to a measure Probabilistic interpretations
3.	Product measure, Fubini's and Tonelli's theorems Riemann-Stieltjes integral
4.	L^p avaruudet

Study material

Type	Name	Author	ISBN	URL	Edition, availability, ...	Examination material	Language
Book	Real Analysis	Royden, H. L.					English
Book	Real and Complex Analysis	Rudin W					English
Summary of lectures	Lebesgue measure and integration	S-L Eriksson, and Pasi Vahimaa,					English

Correspondence of content

More precise information per implementation

	Description	Methods of instruction	Implementation
Implementation 1

Last modified	03.06.2009
Modifier	Sirkka-Liisa Eriksson