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 Monday from 13.00-15.00 in room K11
Exercises are on Wednesday from 13.00-15.00 in room K11. Each week the
exercises (for that week) will be posted on this webpage.
There will be a Take-Home Midterm exam and a Take-Home Final exam.
MidTerm Take-home exam is due April 19, takehome.ps,
takehome.pdf
Take-home Final exam is due June 30 , takehomefinal.ps,
takehomefinal.pdf
Final grade=1/3 (lower grade)+ 2/3 (higher grade), where lower grade=min(midterm,
final) and higer grade=max(midterm, final).
EXERCISES:
(section 1.1 - Riemann Integration) Exercises1.ps , Exercises1.pdf
(section 1.2 - Riemann-Stieltjes Integration) Exercises2.ps , Exercise2.pdf
(section 2.1 - Outer Lebesgue measure) Exercises3.ps , Exercises3.pdf
(section 2.1 - Outer Lebesgue measure, continued) Exercise4.ps, Exercise4.pdf
(section 2.1 - Lebesgue measure) Exercises5.ps , Exercises5.pdf
(section 3.1- sigma-algebras) Exercises6.ps , Exercise6.pdf
(section 3.1+3.2) Exercises7.ps ,Exercises7.pdf
(section 3.2 continued) Exercises8.ps
, Exercises8.dvi
(section 3.2 end) Exercises9.ps, Exercises9.pdf
(section 3.3) Exercises10.ps, Exercises10.pdf
(section 3.3 end) Exercises11.ps, Exercises11.pdf
(section 4.1) Exercises12.ps, Exercises12.pdf
(section 7.1) Exercises13.ps, Exercises13.pdf
(section 8.2) Exercises14.ps, Exercises14.pdf