Measure and Integration
Faculteit  Science and Engineering 
Jaar  2017/18 
Vakcode  WIMIT12 
Vaknaam  Measure and Integration 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Measure and Integration  
Leerdoelen  1. The student is able to describe elementary notions as area and volume in terms of measures. 2. The student is able to reproduce the elementary definitions and facts concerning measurable and integrable functions. 3. The student is able to reproduce the main limiting theorems and to apply them in concrete situations. 4. The student is able to apply the (nontrivial) transformation formulas involving the Jacobian determinant for computing integrals. 5. The student is able to review several examples of standard function spaces of Lebesgue integrable functions. 6. The student is able to outline the theory behind decomposition of measures. 

Omschrijving  Measure and integration offers a general approach to the theory of integration based on measure theory. This is a far reaching extension of the well known theory of Riemann integration. The approach via measures provides a wide variety of applications: in particular about the interchange of various limiting procedures. The development via measurable functions is inspired by probability theory. It provides the necessary basis for a rigorous understanding of stochastic processes. Also, a connection with functional analysis is provided via the introduction of spaces of Lebesgue integrable functions.  
Uren per week  
Onderwijsvorm  Hoorcollege (LC), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(The final grade is determined on the basis of the grades of the 3 homework assignments and the written examination: the average of the three homework assignments counts for 40%, the written exam counts for 60%.) 

Vaksoort  bachelor  
Coördinator  D. Rodrigues Valesin, PhD.  
Docent(en)  D. Rodrigues Valesin, PhD.  
Verplichte literatuur 


Entreevoorwaarden  The course requires previous knowledge of: countable and uncountable sets, sequences of series of real numbers and related convergence notions, and the analysis of realvalued functions defined on the real line; all these notions are acquired in the Analysis course. In the Analysis course, students are also expected to have acquired the ability of explaining and elaborating mathematical proofs. Skills in differentiating and integrating realvalued functions are also needed, and they are acquired in Calculus 1 and 2.  
Opmerkingen  The course is highly desirable for a Master's programme in Mathematics. It is essential for students who pursue more advanced courses in Analysis, Probability Theory and Stochastic Processes.  
Opgenomen in 
