Riemann Integration
→ Let be bounded. By a partition of we mean a collection of finite points
with points
Then we define,
Define
is said to be Riemann integrable if
→ Define by,
→ Let be a seq. of Riemann integrable functions on
If pointwise. Then what you can say about ?
→ let be a set of rational in
Consider
Then is Riemann integrable with
pointwise
→
For a set , we define called the characteristic function of by
Let , then
,
Denote by the length we already know that is, for
Denote by the collection of all intervals in
Then
Question: Does there exist function ((Power set of )) s.t.
- ,
- , where
Side Note:
(per-mod-vity)
- If , for then
Consequence:
- If then