Measure and Integration (2005)
 

Intended audience: third-year students

Textbook: A Concise Introduction to the Theory of Integration D.W. Stroock, Birkhauser, Boston, third edition, 1999

Outline: An introduction to abstract measure and integration theory.

Prerequisites: Standard first and second-year analysis courses.

Main subjects: Riemann integration (retrospective), Lebesgue measure in Euclidean space, measure and integration in abstract spaces, products of measures,  changes of variable, basic inequalities, Radon-Nikodym

Lectures are on Tuesday from 15.00-17.00 in BBL 107a  (except for March 15, the lecture will be in BBL 105b).
Exercises are on Wednesday from 13.00-15.00 in K11.  Each week the exercises (for that week) will be posted on this webpage.

There will be a  Midterm exam and a  Final exam.  Each exam counts for 50% of the final grade.

-No classes on Wednesday March 23 and Tuesday March 29 (hertentamen periode).

-Mid-term exam is on Tuesday April 19 from 14-17 in BBL 105B (it is an open book exam, but you are only allowed to use the book of Strook) .

-PLEASE READ: In period 4 (starting from week 17) the room on Tuesday is changed to BBL 160.

-There will be classes on Tuesday May 17 and Wednesday May 18 (hertentamen perioden-please contact me if you cannot attend).

-There will be NO classes on Tuesday June 7 and Wednesday June 8.

-There will be NO classes on Tuesday June 28 and Wednesday June 29.

-Final exam is on Tuesday July 5 from 14-17 in BBL 105B (open book, you are allowed to use the book of Strook and notes (exercises) taken during the lectures).





EXERCISES:

(section 1.1 - Riemann Integration)  Exercises1.psExercises1.pdf

(section 1.2 - Riemann-Stieltjes Integration) Exercises2.psExercises2.pdf

(section 2.1 - outer Lebesgue measure) Exercises3.ps, Exercises3.pdf

(section 2.1 - Lebesgue measure) Exercises4.ps, Exercises4.pdf

(section 2.1 - Lebesgue measure continued) Exercises5.ps, Exercises5.pdf

(section 3.1- sigma-algebras)  Exercises6.ps, Exercises6.pdf

(section 3.1-continued) Exercises7.ps, Exercises7.pdf

(section 3.2 -construction of integrals) Exercises8.ps, Exercises8.pdf

(section 3.2-continued (material after mid-term) Exercises9.ps, Exercises9.pdf

(section 3.3-convergence of integrals) Exercises10.ps, Exercises10.pdf

(section 3.3-continued) Exercises11.ps, Exercises11.pdf

(section 3.3- the end) Exercises12.ps, Exercises12new.pdf

(section 4.1-product measures) Exercises13.ps, Exercises13.pdf

(section 4.1 + 7.1-Hilbert spaces) Exercises14.ps, Exercises14.pdf

(section 7.1 +8.2) Exercises15.ps, Exercises15.pdf

(section 8.3) Exercises16.ps, Exercises16.pdf

Extra Exercises
extraexercises.ps,extraexercises.pdf





SOLUTIONS:


Solutions1.ps
Solutions1.pdf

Solutions2.ps, Solutions2.pdf

Solutions3.ps, Solutions3.pdf

Solutions4.ps, Solutions4.pdf

Solutions5.ps, Solutions5.pdf

Solutions6.ps, Solutions6.pdf

Solutions7.ps, Solutions7.pdf

Solutions8.ps, Solutions8.pdf

Solutions9.ps, Solutions9.pdf

Solutions10.ps, Solutions10.pdf

Solutions11.ps, Solutions11.pdf

Solutions12.ps, Solutions12.pdf

Solutions13.ps, Solutions13.pdf

Solutions14.ps, Solutions14.pdf

Solutions15.ps , Solutions15.pdf

Solutions16.ps, Solutions16.pdf

Solutionsextraexercises.ps, Solutionsextraexercises.pdf