## Re: [harmonic] Property for Haar measure!!

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• In some compact groups, you have $G = G^2$, so that you can get $lambda(G) = lambda(G^2)$. Michael ... --
Message 1 of 3 , Dec 5, 2004
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In some compact groups, you have $G = G^2$, so that you can get
$\lambda(G) = \lambda(G^2)$.

Michael

On Sat, 4 Dec 2004, ali akbar arefigamal wrote:

> Hi, all
>
> Let G be a LCA group with the Haar measure $\lambda$. Can we find
> a measurable subset A (having finite measure )in G such that
> $\lambda(A)=\lambda(A^{2})$, in which $A^{2}=\{a^{2}, a\in A\}$ .
>
> I think this is false, but i cann't prove it. It is possible hint me.
>
> Thanks,
>
>
> ---------------------------------
> Do you Yahoo!?

--
_______________________________________________________________________
| |
| Professor Michael Cowling School of Mathematics |
| Telephone: +61 2 9385 7101 University of New South Wales |
| Fax: +61 2 9385 7123 UNSW Sydney NSW 2052 |
| Mobile: +61 4 0936 0678 AUSTRALIA |
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• one may even take S^1= multiplicative group of all complex numbers with modulus 1.every element in it is a square! --- In harmonicanalysis@yahoogroups.com,
Message 2 of 3 , Feb 28, 2005
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one may even take S^1= multiplicative group of all complex numbers
with modulus 1.every element in it is a square! --- In
harmonicanalysis@yahoogroups.com, Michael Cowling <michaelc@m...>
wrote:
>
> In some compact groups, you have $G = G^2$, so that you can get
> $\lambda(G) = \lambda(G^2)$.
>
> Michael
>
>
>
> On Sat, 4 Dec 2004, ali akbar arefigamal wrote:
>
> > Hi, all
> >
> > Let G be a LCA group with the Haar measure $\lambda$. Can we
find
> > a measurable subset A (having finite measure )in G such that
> > $\lambda(A)=\lambda(A^{2})$, in which $A^{2}=\{a^{2}, a\in A\}$ .
> >
> > I think this is false, but i cann't prove it. It is possible
hint me.
> >
> > Thanks,
> >
> >
> > ---------------------------------
> > Do you Yahoo!?
> > Yahoo! Mail - now with 250MB free storage. Learn more.
>
> --
>
_____________________________________________________________________
__
> |
|
> | Professor Michael Cowling School of Mathematics
|
> | Telephone: +61 2 9385 7101 University of New
South Wales |
> | Fax: +61 2 9385 7123 UNSW Sydney NSW
2052 |
> | Mobile: +61 4 0936 0678 AUSTRALIA
|
> | UNSW is a registered CRICOS provider, code
00098G |
>
|____________________________________________________________________
___|
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