Multiresolution Analysis scaling function

Question

Given a multiresolution analysis $(V_j)_{j\in \mathbb{Z}}$ in $L²(ℝ)$ with scaling function $\varphi \in L²(ℝ)$. As $(2^{1/2}\varphi(2t-k))_{k\in \mathbb{Z}}$ is an orthonormal basis of $V_1$ and $\varphi \in V_0\subseteq V_1$ we have $$\varphi(t)= \sum\limits_{k\in \mathbb{Z}}^{}\langle\varphi, 2^{1/2}\varphi(2t-k)\rangle 2^{1/2}\varphi(2t-k).$$ This equation is called scaling equation. Does this equation hold for almost every $t\in ℝ$? And if yes, why?