  We investigate some properties and convergence theorem of
Kluv\'{a}nek-Lewis-Henstock $\m-$integrability for $\m-$measurable functions
that we introduced in \cite{ABH}. We give a $\m-$a.e. convergence version of
Dominated (resp. Bounded) Convergence Theorem for $\m.$ We introduce
Kluv\'{a}nek-Lewis-Henstock integrable of scalar-valued functions with respect
to a set valued measure in a Banach space. Finally we introduce $(KL)-$type
Dominated Convergence Theorem for the set-valued Kluv\'{a}nek-Lewis-Henstock
integral.
