Re: Measure termnology

On May 4, 6:02 pm, Jules <julianro...@xxxxxxxxx> wrote:
On May 4, 5:35 pm, "Stephen J. Herschkorn" <sjhersc...@xxxxxxxxxxxx>
wrote:

With reference to a Borel measure, is there an adjective that means
"every compact set has finite measure"? On R^n, Lebesgue and
probability measures would have this property; on the reals, the
measure A |-> integral(x in A, 1/x^2) would not.

--
Stephen J. Herschkorn sjhersc...@xxxxxxxxxxxx
Math Tutor on the Internet and in Central New Jersey and Manhattan

I do not know the answer to your question. However, if the space in
question is locally compact (such as R^n), then every compact set has
finite measure if and only if every point has a neighborhood with
finite measure. I don't know if this term is used, but is might be
reasonable to call such a measure "locally finite."

I just looked it up on Wikipedia, and the term "locally finite
measure" is used the way I suggested.

.

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