I'm reading a one proof. This say
If $u$ is a test function (smooth function with compact support), then $$|\delta_0(u)|=|u(0)|=\left|\int_{—1}^0u'(t)dt\right|\leq \lVert u'\rVert_p\leq \lVert u\rVert_{W^{1,p}(-1,1)}.$$ By density of test function, we can extend $\delta_0$ to the functions of $W^{1,p}(-1,1)$.
I don't understand this "By density of test function, we can extend $\delta_0$ to the functions of $W^{1,p}(-1,1)$".
Please, Anybody will be able to explain me?