Re: Improper distribution



On Jan 28, 6:56 am, "Inf" <infinitysqua...@xxxxxxxxx> wrote:
Intuitively, I would expect something like a delta function at
infinity,
But does that have any meaning? When does it contribute to an
integral i.e. an expectation, given the way an integral is defined,
as a limit towards the upper end point.

I'll admit, I've never seen this done with the delta at infinity.
Certainly with a delta at a finite value, it works fine. I think the
thing with it at infinity would be that you'd have to be careful in
how you do integrals, and consider on a case-by-case basis whether or
not it should be included.

You might be better just treating this as two distributions.

Michael

.

Relevant Pages

  • Re: improper integrals
    ... basic concepts relating to improper integrals. ... Does the integral from 0 to infinity of x converge or diverge? ...
    (sci.math)
  • Re: Why does everyone do it?
    ... minus infinity to plus infinity, ... If you then take the limit of these integrals as n approaches ... are being mis-used with mainstream mathematics. ... finite domain for a moment, then it's easily spotted what goes wrong. ...
    (sci.math)
  • Re: derivatives of power series
    ... textbook would convert it to 1, other times, it would keep it at 0. ... But on the wikipedia site, it showed that TWO scenarios are possible. ... n now goes from 1 to infinity, ... Likewise, for integrals, I wouldn't even look at their formulas. ...
    (sci.math)
  • Re: Riemann-Lebesgue lemma
    ... does anybody know if there is a result that tells how fast the Fourier transform of a function satisfying a Lipschitz condition tends to zero as the variable approaches infinity? ... don't say anything about integrals over sets with infinite ...
    (sci.math)
  • Re: Renormalization
    ... > momentum cutoff that you later take the limit as it goes to infinity. ... integrals we are talking about actually diverge. ... To do that we need to regularize and there is more than one ...
    (sci.physics.research)