Riemann-Stieltjes integral
Let and be bounded, real-valued functions defined upon a closed finite interval of , a partition of , and a point of the subinterval . A sum of the form
is called a Riemann-Stieltjes sum of with respect to . is said to be Riemann Stieltjes integrable with respect to on if there exists such that given any there exists a partition of for which, for all finer than and for every choice of points , we have
If such an exists, then it is unique and is known as the Riemann-Stieltjes integral of with respect to . is known as the integrand and the integrator. The integral is denoted by
Title | Riemann-Stieltjes integral |
---|---|
Canonical name | RiemannStieltjesIntegral |
Date of creation | 2013-03-22 12:51:13 |
Last modified on | 2013-03-22 12:51:13 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 11 |
Author | Mathprof (13753) |
Entry type | Definition |
Classification | msc 26A42 |
Related topic | RiemannSum |
Related topic | IntegralSign |
Defines | Riemann-Stieltjes sum |
Defines | integrator |