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I have a metric space with a probability measure (implying that the measure is regular). What conditions should I ask of the measure or of the metric to get that a function in $\mathcal{L}^2(d\mu)$ can be approximated in $\mathcal{L}^2$ by a uniformly continuous function?

Thanks

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    Can you define precisely what you mean by "regular"? Conventions vary.2011-02-04

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