A is the open unit ball in R^n. Let B be the compliment of A (R^n\A).(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integrable function proof

**Physics Forums | Science Articles, Homework Help, Discussion**