1. Dec 19, 2009

### dinhism

1. The problem statement, all variables and given/known data
For each description below, provide a specific example fitting the description (provide some justification), or else explain why no such example exists.

1)An open set with no accumulation point

2)A subset of [0,\sqrt{2}] of Lebesgue measure 1 which contains no interval

3)A subset of [0,sqrt{2}] of Lebesgue measure 1 with no accumulation point

4)A bounded set with Lebesgue measure infinity

5)An open set with Lebesgue measure 0

6)A function that has all its derivative at p = 3 but is not analytic there

7)A sequence of functions on $R$, all continuous everywhere, all non differentiable at 0, that converge uniformly to a function differentiable everywhere

8)A series of functions which converges to (sin[3x])/x

2. Relevant equations

3. The attempt at a solution