Stochastic and other functional integrals (Q803310)

For a fixed real number a, the space T of all real-valued functions f on \([a,\infty)\) with \(f(a)=0,\) and a fixed \(F\in L^ 2(a,\infty),\) the paper discusses integrals \((1)\quad \int^{\infty}_{a}F(t)df(t)\quad (f\in T).\) \textit{T. W. Lee} [J. Austral. Math. Soc., Ser. A 21, 64-71 (1976; Zbl 0314.28009)] uses Wiener measures on T, showing that a gauge- defined integral (1) equivalent to that of \textit{R. E. A. C. Paley}, \textit{N. Wiener} and \textit{A. Zygmund} [Math. Z. 37, 647-668 (1933; Zbl 0007.35402)] exists for almost all \(f\in T.\) A gap in the proof is filled by the present paper which uses a more general non-negative measure than Wiener's, and gives properties of (1) such as a Saks-Henstock lemma. There may not be an inequality like that of Weierstrass in Burkill integration, but a variational integral can be defined using variation sets. - Note that on p. 467 the first f on each of lines 16 to 18 should be F. Similarly on p. 469 line -4.