Integral bases in linear topological spaces

The fredholm and volterra problems for stieltjies integral equations

“…For convemence some of the definitions and results from [73 are reproduced here. DEFINITION 1 ( [7], Definition 1). Suppose P is a non-void collection of subsets of A ' .…”

“…be said to have the permanence property. It is shown jn [7], Example l j fh.at given any pmto-algebra U p there exists a choice function subolvision of . x ,r:d t 2nd s ZTe in q 2, fs: some f then thez c:&s 9-subdivisions E and F which refine @ and s x h that for some c", E E and -Fk E F, q(Ej) -t an$ {p(Fk) = J.…”

Properties of Q(X,P) spaces

“…We will now show that The proof will be complete once it is shown that (3) implies (1). Let be a fundamental net of points.…”

“…The representation of linear operators on Q(X,P) spaces when X is an interval or the real line has been considered by Kalteiiborn [14], Hildebrandt [11], Lane [17] and [18], and Baker [1]. Dyer in [3] and [5] has considered the abstract operator representation problem. The problem of solving linear operator equations in special Q(X,P) spaces has been considered in numerous papers by McNerney, Hinton, Hildebrandt, and Lane.…”

“…The above integral is known as the iJf integral and was introduced and developed by J. A. Dyer in [3], [4], and [5]. The following two theorems are very important for the remainder of this work and both results can be found in [5] .…”