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If $X$ is a metric space, $m$ is a Borel probability space on $(X,\mathscr{B})$ where $\mathscr{B}$ is the $\sigma$-algebra generated by open sets on $X$, can we prove that the space $L^{2}(X,\mathscr{B},m)$ is spearable?

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This post answers your question precisely: https://mathoverflow.net/a/42383.

I am not able to post this answer as a comment as I do not have 50 reputation yet.

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  • $\begingroup$ Thanks for your answer.I have read the webpage you paste,but I have some difficulty in understanding. Would you like to give some more detail? Or recommend some related material. $\endgroup$ – Yee Neil Apr 30 '14 at 1:05

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