$$ s(t)x(t) = \sum_{n=-\infty}^{\infty} \delta(t - nT_s)x(t) \newline = \sum_{n=-\infty}^{\infty} \delta(t - nT_s)x(nT_s)
$$
Nyquist-Shannon Theorem: Let $x$ be a bandlimited CT signal with bandwidth $B$. If $x$ is sampled with sampling period $T_s$ satisfying $T_s ≤ \frac{1}{2B}$ then $x$ can b exacly recovered from the samples