The Vector Space of Riemann Integrable Functions - Real Analysis | Lecture 18

In this lecture we prove that the space of Riemann integrable functions is a vector space. We further see that the Riemann integrable can be interpreted as a linear functional, which is a function that maps from a vector space into the real numbers. We further prove that Riemann integrals can be broken up over a domain into integrals over smaller intervals and then added back together to obtain the desired full integral. All proofs are given in full detail to fully illustrate the definition of Riemann sums and Riemann integrals from the previous lecture.

This course is taught by Jason Bramburger.