#11 (due Mon., 11/18) Problems 4.5 and 4.7, page 85
#10 (due Mon., 11/11) Problem 4.2, page 85
#9 (due Mon., 11/4) Prove that
(1) If a simple function is defined on disjoint sets, then the
integral is independent of the representation, and
(2) If a simple function is defined on two non-disjoint sets,
then it can be decomposed into three disjoint sets
without affecting the integral.
#8 (due Mon., 10/28) 3.28 a,b and 3.29 (pp.71-73)
#7 (due Mon., 10/21)
in-class problem 2.48 (5-10 minutes) and
proof that an increasing function on a measurable
domain is measurable.
#6 (due Mon., 10/7) in-class presentation of proof from section 3.5
#5 (due Mon., 9/30) prob. 16 (page 66)
#4 (due Mon., 9/23) prob's 11 & 14 (page 64)
#3 (due Mon., 9/16)
Heine-Borel proofs,
2 border examples (open/closed sets),
the Cantor ternary set is closed and uncountable
#2 (due Mon., 9/9) 3 border examples (for Heine-Borel and Prop.16)
#1 (due Wed., 9/4) outer measure of rationals and prob's 5 & 8 (p.58)
Unless specified otherwise, homework will be assigned during class and will be collect the following Monday.
Occasionally, you may discover over the weekend that you need to ask me questions about the homework. In this case, you may certainly ask the questions on Monday and request an extension (until Wednesday).
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