Integral with Dirac delta.

Question

Let $\mu= \sum_{k=0}^{\infty} \frac{1}{2^k}\delta_k$. Calculte the integral : $ \int_{\mathbb{R}^2} [2^{-x^2-y^2}+\frac{3}{4} ] dL^1(x) \otimes d\mu(y)$. Where $[a]$-floor.

Can I write : $\int_{-\infty}^{\infty} \left( \int_{-\infty}^{\infty}[2^{-x^2-y^2}+\frac{3}{4} ] dL^1(x) \right) d\mu(y)$?