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Math Help - Product sigma algebra of a non-separable space

  1. #1
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    Product sigma algebra of a non-separable space

    Hi, following is the question I have been thinking about for a while -

    Is \mathcal{B}(l_\infty \times l_\infty) = \sigma(\mathcal{B}(l_\infty) \times \mathcal{B}(l_\infty))?

    Can anyone help me on this? Thanks a lot.
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  2. #2
    Super Member girdav's Avatar
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    Re: Product sigma algebra of a non-separable space

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    Re: Product sigma algebra of a non-separable space

    Thanks girdav. I have taken a look at this link but it doesn't specifically answer the question about l_\infty
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  4. #4
    Super Member girdav's Avatar
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    Re: Product sigma algebra of a non-separable space

    Michael Greinecker's answer can be used since \ell^{\infty} has the same cardinality as \mathbb R.
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    Re: Product sigma algebra of a non-separable space

    Right. Thanks a lot. I will read the bits in detail.
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    Re: Product sigma algebra of a non-separable space

    Quote Originally Posted by girdav View Post
    Michael Greinecker's answer can be used since \ell^{\infty} has the same cardinality as \mathbb R.
    Hi girdav, I read the link again. The doubt I have is the theorems says that for spaces with cardinality greater than 'c' we have the non-equality. But from what I understood, he doesn't prove the equality for all spaces with cardinality equal to 'c'. Am I missing something?
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