p-Lambda-bounded variation

Document Type : Research Paper



A characteriation of continuity of the $p$-$Lambda$-variation function is given and
the Helly's selection principle for
$Lambda BV^{(p)}$ functions is established.
A characterization of the inclusion of Waterman-Shiba classes into
classes of functions with given integral modulus of continuity is given.
A useful estimate on modulus of variation of functions of class $Lambda
BV^{(p)}$ is found.