Adjoint classes of Lebesgue-Stieltjes integrable functions (Q1852381)

The author obtains several adjoint classes of functions for the Lebesgue-Stieltjes integral with respect to a measure defined by a Borel measurable function that is of extended bounded variation on\([a,b]\); that is of bounded variation on each \([a,x], a\leq x<b\), and either the positive or negative variation is finite on \([a,b]\). The adjoint classes in the class of all Borel measurable functions are: (1) bounded functions and functions of bounded variation; (2) \(L^q\) functions and functions that have absolutely continuous right regularizations and derivatives in \(L^p, 1\leq p\leq \infty, 1/p + 1/q= 1\); (3) the class of functions such that for some \(M\) all closed subsets of \(\{x; |f(x)|>M\}\) are countable and the class of functions that have right regularizations that are continuous and of bounded variation.