Measure Theory and Integration (MA40042)
Semester I, 202021
Content:
Systems of measurable sets: sigmaalgebras, pisystems, dsystems,
Dynkin's Lemma, Borel sigmaalgebras. Measure in the abstract: convergence properties, Uniqueness Lemma, Caratheodory's Theorem (statement). Lebesgue outer measure and measure on Rn. Measurable functions. MonotoneClass Theorem. Probability. Random variables. Independence. Integration of nonnegative and signed functions. MonotoneConvergence Theorem. Fatou's Lemma. DominatedConvergence Theorem. Expectation. Product measures. Tonelli's and Fubini's Theorem. RadonNikodym Theorem (statement). Inequalities of Jensen, Holder, Minkowski. Completeness of Lp.
Books
News
This site to be used in conjunction with the course Moodle page.
Lecture notes
 Pages 1 to 10 (Intro and Sections 13): pdf file.
 Pages 11 to 16 (Sections 45): pdf file.
 Pages 17 to 22 (Sections 67): pdf file.
 Pages 23 to 27 (Section 8): pdf file.
 Pages 28 to 31 (Section 9): pdf file.
 Pages 32 to 34 (Section 10): pdf file.
 Pages 35 to 37 (Section 11): pdf file.
 Pages 38 to 41 (Section 12): pdf file.
 Pages 42 to 45 (Section 13): pdf file.
 Pages 46 to 49 (start of Section 14): pdf file.
 Pages 50 to 53 (End of Section 14, and Section 15):
pdf file.
 Pages 54 to 61 (Sections 1617):
pdf file.
Problem sheets
Solutions
A mock online paper

This mock exam
is adapted from last year's exam (i.e. the exam 201920 Semester 1).

Last year's exam was closedbook. The new Mock exam is designed for this year's openbook format.

Parts of questions that could be answered by copying material
from the typed notes or solutions to exercises have been replaced
by unseen material of a similar level of difficulty.

Both the `new' Mock exam questions, and the `Old'
questions as they appeared in last year's exam,
have been included for comparison purpuses.

NB the mock exam paper has not been through a checking process in the way that actual papers are qualitycontrolled.