  For a positive integer $r$, a distance-$r$ independent set in an undirected
graph $G$ is a set $I\subseteq V(G)$ of vertices pairwise at distance greater
than $r$, while a distance-$r$ dominating set is a set $D\subseteq V(G)$ such
that every vertex of the graph is within distance at most $r$ from a vertex
from $D$. We study the duality between the maximum size of a distance-$2r$
independent set and the minimum size of a distance-$r$ dominating set in
nowhere dense graph classes, as well as the kernelization complexity of the
distance-$r$ independent set problem on these graph classes. Specifically, we
prove that the distance-$r$ independent set problem admits an almost linear
kernel on every nowhere dense graph class.
