Class Contents

• Convergence of power series
• A nowhere differentiable function

Remark:

We can also use this to reprove the differentiability of power series.

Proof.

Remark:

Now we can use the results with uniform convergence to construct some interesting functions:

1. a nowhere differentiable function
2. a space-filling curve

Proof.

A nowhere differentiable function

But, one of the following holds:

Space-filling Curves

Analysis WebNotes by John Lindsay Orr.
Comments to the author: jorr@math.unl.edu

All contents copyright (C) 1996 John L. Orr
University of Nebraska--Lincoln
All rights reserved

Last modified: June 1996