Q:

Delta de Dirac Function linear?

Show that $\delta_0$, Dirac function, defined than $\left<{\delta_0,\phi}\right> = \phi(0)$ is linear.
I trying: Let be $\phi_1,\phi_2$ $\in W^{m,p}(\Omega)$ then $\delta_0(\phi_1+\phi_2)=(\phi_1+\phi_2)(0)$, but I need more steps.

A:

Hint: What is the definition of a linear functional?  Just plug this into the definition and see if it works.  Under trying, $(\phi_1 + \phi_2)(0)=\phi_1 (0) + \phi_2 (0)$

