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Topic: Various definitions of integral
Replies: 1   Last Post: Sep 2, 2011 10:12 PM

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Stephen J. Herschkorn

Posts: 2,297
Registered: 1/29/05
Various definitions of integral
Posted: Sep 2, 2011 8:29 PM
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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 sjherschko@netscape.net
Math Tutor on the Internet and in Central New Jersey and Manhattan

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