Analysis WebNotes
arrow_back arrow_forward

Class Contents

Remark:

Thus, uniform limits are unique.

Example:
Example:
The first example illustrates a useful test:

Example:

The best application of uniform convergence is to construct new functions from approximating sequences. Pointwise convergence does this too, but uniform limits inherit more of the useful properties of the approximating functions.

Proof.

Example:

Proof.

Remark:
In order to use that last result in a nontrivial way, we need to be able to recognize uniformly converging sequences when we don't know the limits.

Proof.