Math 6211, N. Falkner
Homework Set 1
Autumn Semester, 2015
Fourier Series Motivated Modern Analysis.
This is a course on the general topic of real analysis, so you might well ask Why begin with the specic
topic of Fourier series? One answer is that while

Math 6211, N. Falkner
Homework Set 14
Autumn Semester, 2015
Continuous Bilinear Maps.
abc
done 14W
Exercise 363. Let U , V , and W be normed linear spaces. Let B : U V W be bilinear. Prove that
the following are equivalent:
(a) There is a constant M such

Math 6211, N. Falkner
Homework Set 13
Autumn Semester, 2015
More About the Pseudometric Space of Measurable Sets.
Due 14Th
Exercise 350. Let (X, A , ) be a measure space and let E be the set of all E A such that (E) < .
Dene : E E [0, ) by (E, F ) = (E F