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:
 * $\forall \alpha, \beta \in \R: T \left({f + g}\right) = T \left({f}\right) + T \left({g}\right)$

Proof
From Integral Operator is Linear:


 * $\forall \alpha, \beta \in \R: T \left({\alpha f + \beta g}\right) = \alpha T \left({f}\right) + \beta T \left({g}\right)$

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