York University
MATH 6280 3.00AF Measure Theory
Assignment 2
Due October 21, 2013 in class, or in my N520 mailbox by 10am on October 22.
Do four of the following six problems, and hand them in.
(1) Let 1 and 2 be outer measures. Show that (A) = max(1 (A),
York University
MATH 6280 3.00AF Measure Theory
Assignment 4
Due December 6, 2013 in class.
Do four of the following six problems, and hand them in.
(1) Let Bt () be a Brownian under a probability measure P (d). Let be
the random set of times 0 t 1 such t
York University
Faculty of Graduate Studies
MATH 6280 3.00AF Measure Theory
Midterm Examination Solutions (Salisbury)
October 24, 2013
Justify all your work.
(1) [10] Let X = cfw_1, 2, 3, 4 and let F be the smallest -algebra of subsets of X
that includes
York University
MATH 6280 3.00AF Measure Theory
Assignment 3
Due November 20, 2013 in class, or in my N520 mailbox.
Do four of the following six problems, and hand them in.
(1) Let (X, F, ) be a measure. Let f 0 be measurable and dene the
measure (A) = A
York University
Faculty of Graduate Studies
MATH 6280 3.00AF Measure Theory
Instructor: T. Salisbury
Final / Comprehensive Examination Solutions
December 19, 2013
Justify all your work. You may use any result proved in class or the text, but if you do so,
York University
MATH 6280 3.0AF (Measure Theory)
Assignment 1
Due in class, October 2, 2013
Do 5 of the following 7 problems.
(1) Let f : R R be any function. Show that cfw_x | f is continuous at x is a G
set.
(2) Let f1 and f2 be functions R R. Suppose t