A is the open unit ball in R^n. Let B be the compliment of A (R^n\A). If f: B -> R is defined by f(x) = ||x||^-3... (where x is in B) For n=2, using an increasing union of compact sets show that f is integrable on B. For n=3, show that f is not integrable. ____________________________________________ Does an increasing union of sets here mean that each compact set must be contained entirely in the next? It seems clear here that f will be bounded for n=2 (from 0 to 1), and thus would suggest that it is integrable, but then why not n=3? I seem to be missing a requirement for f being integrable here, any help would be appreciated.