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Re: [harmonic] Property for Haar measure!!

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  • Michael Cowling
    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,
      >
      >
      > ---------------------------------
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      --
      _______________________________________________________________________
      | |
      | 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 |
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    • rauindia
      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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