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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

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A different version of Besicovitch Covering Theorem involving balls of half radius

Are you allowing $b$ to depend on the manifold (as it appears to me from your statement)? In that case, Besicovitch is overkill, and this statement holds in much more generality than Besicovitch. One …
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