| 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(A ∩ B) + φ(A ∪ B) = φ(A) + φ(B). | |
| n | manditory problem |
| ∗n | manditory problem, not from text |
| (n) | helper problem |
| [n] | ungraded problem |
| [∗n] | ungraded problem, not from text |
| {n} | optional problem |