# Questions related to homeomorphisms of R^n

1. Jul 21, 2012

### coquelicot

Hello,

I have 3 questions related to homeomorphisms ℝ^n to ℝ^n:

1) Is the following generalization of the Lebesgue theorem true?
Every homeomorphism ℝ^n to ℝ^n is differentiable almost everywhere.

2) Assuming the answer to 1) is negative, is the composition of two
almost everywhere differentiable homeomorphisms differentiable almost everywhere?

3) Assuming the answer to 1) is negative, is the invert of a differentiable almost everywhere homeomorphism differentiable almost everywhere?

thx.