While the Riemann, Lebesgue and general abstract integral are most common, there are quite a few other definitions of integral. See, for example, http://en.wikipedia.org/wiki/Integral#Other_integrals . Is there a case of a subset S of R^n and a function f:: S -> R such that the integral of f over S under two definitions both exist yet take on distinct values? I mean, other than those where the underlying measures or the "with-respect-to" functions (e.g., in the case of Stieltjes integrals) differ.
-- Stephen J. Herschkorn firstname.lastname@example.org Math Tutor on the Internet and in Central New Jersey and Manhattan