Course Catalog 2006-2007

MAT-41296 MEASURE AND INTEGRATION THEORY, 7 cr
Measure and Integration Theory

Courses persons responsible
Sirkka-Liisa Eriksson

Lecturers
Sirkka-Liisa Eriksson

Language of Instruction
Instruction of exercises in English

Objectives
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       

Requirements for completing the course
Written examination

Evaluation criteria for the course

  • Used assessment scale is numeric (1-5)

    • Study material
    Type Name Auhor ISBN URL Edition, availability... Exam material Language
    Book Real and Complex Analysis Rudin W       No  English 
    Book Real Analysis Royden, H. L.       No  English 
    Summary of lectures Lebesgue measure and integration S-L Eriksson, and Pasi Vahimaa,       No  English 

    Prerequisites
    Prequisite relations (Sign up to TUT Intranet required)

    Remarks

  • The course is suitable for postgraduate studies.

  • Course will not be lectured in the academic year 2006-2007.

    • Correspondence of content
    MAT-41290 Measure and Integral Theory

    Last modified 03.04.2006
    Modified byEmilia Ylirinne