A characterization theorem for the existence of a Hellinger-type integral. (English) Zbl 0879.28007

Assume that on an interval \([a,b]\) real functions \(h\) and nondecreasing \(m\) are given such that if \([p,q] \subset [a,b]\) and \(m(q) - m(p)=0\) then \(h(q) - h(p)=0\). Necessary and sufficient conditions are presented for the existence of the Hellinger-type integral \[ \int_a^b \frac { df dh}{dm} \] where \(f\) is a quasi-continuous real function on \([a,b]\).


28A25 Integration with respect to measures and other set functions