A function f: ℝⁿ → ℝ satisfies the condition $Q_i\left(x\right)$ (resp. $Q_s\left(x\right)$, $Q_o\left(x\right)$) at a point x if for each real r > 0 and for each set U ∋ x open in the Euclidean topology of ℝⁿ (resp. strong density topology, ordinary density topology) there is an open set I such that I ∩ U ≠ ∅ and $|(1/\mu \left(U\cap I\right)){\int }_{U\cap I}f\left(t\right)dt-f\left(x\right)|<r$. Kempisty’s theorem concerning the product quasicontinuity is investigated for the above notions.