Definition:Definite Integral/Riemann/Integral Operator

Definition

Let $C \closedint a b$ be the space of continuous functions.

Let $x \in C \closedint a b$ be a Riemann integrable function.

Let $\R$ be the set of real numbers.

The Riemann integral operator, denoted by $I$, is the mapping $I : C \closedint a b \to \R$ such that:

$\ds \map I x := \int_a^b \map x t \rd t$

where $\ds \int_a^b \map x t \rd t$ is the Riemann integral.

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 2.1$: Continuous and linear maps. Linear transformations