= Locality of distributions
A <distribution> which vanishes on a neighborhood of each point vanishes globally. To prove this, choose a smooth <partition of unity> subordinate to the neighborhoods. Every <test function> is a finite sum of its products with the partition members, since its <support> is compact. The <distribution> vanishes on each summand. Applying the result to a difference proves that two <distributions> agreeing locally agree globally. This justifies defining the <support of a distribution> by removing the union of all open regions on which it is zero.
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Target: Periodic primitive with zero mean. Parent: Periodic extension. Intended file: function.bigb.
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