We prove an extension of Bourgain's theorem on pinned distances in measurable subsets of $mathbb{R}^2$ of positive upper density, namely Theorem $1^prime$ in cite{B}, to pinned non-degenerate $k$-dimensional simplices in measurable subsets of $mathbb{R}^{d}$ of positive upper density whenever $dgeq k+2$ and $k$ is any positive integer.