Re: completion of L^2



David Macmanus wrote:
> In the book 'Lectures on Groups and Spaces For Physicists', Isham says
> that the space L^2 is incomplete but that it can be completed by filling
> in the gaps. I find this misleading. Isn't it the case that completing
> L^2 is simply a matter of changing from the Riemann integral to the
> Lebesgue integral - so in fact we don't need to 'add' anything in the
> case? [But the Lebesgue integral is able to 'see' some (all??) of the
> functions that the Riemann integral misses].
> Thanks,
> David.
>
>
> --
> Posted via Mailgate.ORG Server - http://www.Mailgate.ORG

I don't understand. What's it supposed to mean, L^2 is incomplete? L^2
is complete. The completion of C_C in the L^1-norm is L^1 - is that
what you're talking about with your changing from the Riemann integral
to the Lebesgue integral?

.

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