Andy writes: << . . . [I wrote] << Conversely, there is a chance that a strange singularity can be created near 0, say, of a function f:[0,1} -> R, such that f is EWAP integrable, but not APAP integrable.

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The thing is, once the mesh size is less than 10^-100, the effect of the singularity at 0 is tiny, so the AWAP integral will still converge whenever the EWAP one does. . . .

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Only if you're assuming something about f (like continuity or boundedness), which I wasn't. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele