Intuition of weak star convergence.

Question

Given $\Omega=(0,1)$, consider the following sequence $$ v_j(x)\colon=\begin{cases} \;a &\text{if }jx-\lfloor jx \rfloor\le\theta\\ \;b &\text{otherwise} \end{cases} $$ where $a,b\in\mathbb{R}$ and $\theta\in(0,1)$. Then the $L^\infty-\text{weak}^\ast$ limit of $v_j$ is $\theta a+(1-\theta)b$. Is there any intuitive explanation of why this is the weak$^\ast$ limit of $v_j(x)$?