- ...paper
- This work remained unpublished until 1822.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...sums
- Note. We have tacitly changed the interval to
28#28 for convenience.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...1.
- Recall, (
*m*,*n*) = 1 means*m*and*n*are relatively prime.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...integrable?
- This question of course has been answered. The relevant theorem is this:
**Theorem.***Let*. In the case that*J*be a closed interval. The function*f*(*x*) is R-integrable over*J*if and only if it is continuous almost everywhere-*J**f*is non negative, these conditions in turn are equivalent to the graph of*f*(*x*) being (Jordan) measurable.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...spaces
- To name just a few, there are the Lebesgue, Hardy, Lipschitz, Sobolev, Orlicz, Lorentz and Besov spaces. Each space plays its own unique and important role in some slightly different area of analysis.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...analysis
- And this is an entire area of mathematics in and of itself.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Mon Apr 21 12:31:50 CDT 1997