generalized Riemann integral
Given a gauge , a partition of an interval is said to be -fine if, for every point , the set containing is a subset of
A function is said to be generalized Riemann integrable on if there exists a number such that for every there exists a gauge on such that if is any -fine partition of , then
If then the number is uniquely determined, and is called the generalized Riemann integral of over .
The reason that this is called a generalized Riemann integral is that, in the special case where for some number , we recover the Riemann integral as a special case.
|Title||generalized Riemann integral|
|Date of creation||2013-03-22 13:40:03|
|Last modified on||2013-03-22 13:40:03|
|Last modified by||rspuzio (6075)|
|Defines||generalized Riemann integrable|