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Various definitions of integral
Posted:
Sep 2, 2011 8:29 PM


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 "withrespectto" functions (e.g., in the case of Stieltjes integrals) differ.
 Stephen J. Herschkorn sjherschko@netscape.net Math Tutor on the Internet and in Central New Jersey and Manhattan



