  It is known that for Banach valued functions there are several approaches to
define a Sobolev class. We compare the usual definition via weak derivatives
with the Reshetnyak-Sobolev space and with the Newtonian space; in particular,
we provide sufficient conditions when all three agree. As well we revise the
difference quotient criterion and the property of Lipschitz mapping to preserve
Sobolev space when it acting as a superposition operator.
