  We introduce pointwise measure expansivity for bi-measurable maps. We show
through examples that this notion is weaker than measure expansivity. In spite
of this fact, we show that many results for measure expansive systems hold true
for pointwise systems as well. Then, we study the concept of mixing,
specification and chaos at a point in the phase space of a continuous map. We
show that mixing at a shadowable point is not sufficient for it to be a
specification point, but mixing of the map force a shadowable point to be a
specification point. We prove that periodic specification points are Devaney
chaotic point. Finally, we show that existence of two distinct specification
points is sufficient for a map to have positive Bowen entropy.
