Homework for Math 362A
Spring, 2008


Problem Set

Chapter

Problems

18 ∗27 Suppose, in the proof of Theorem 7.18, we had defined fn to be
       fn(x) = αn φ(4nx),      with 0 < α < 1/4.
Show that f (defined as the infinite sum of the fn, like in the proof) would be differentiable at some real x.
∗28 Let φ be an additive set function on a ring ℜ. If A, B ∈ ℜ, prove that φ(AB) + φ(AB) = φ(A) + φ(B).

Notation

n manditory problem
∗n manditory problem, not from text
(n) helper problem
[n] ungraded problem
[∗n] ungraded problem, not from text
{n} optional problem