Integral Operator is Linear/Corollary 1

Theorem
Let $T$ be an integral operator.

Let $f$ and $g$ be integrable real functions on a domain appropriate to $T$.

Then:
 * $\forall \alpha, \beta \in \R: \map T {f + g} = \map T f + \map T g$

Proof
From Integral Operator is Linear:


 * $\forall \alpha, \beta \in \R: \map T {\alpha f + \beta g} = \alpha \map T f + \beta \map T g$

The result follows by setting $\alpha = \beta = 1$.