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<p>A sum of open sets is a map taking two bounded open sets <i>A</i>, <i>B</i> and producing a new open set <i>A</i> ⊕ <i>B</i>. We prove that, up to sets of measure zero, there is only one such sum satisfying a natural list of axioms. It is the scaling limit of the Diaconis–Fulton smash sum.</p>

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The smash sum is the unique sum of open sets satisfying a natural list of axioms

  • 期刊论文

  • 发表日期：

    2025年1月21日

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  • Hannah Cairns

摘要

A sum of open sets is a map taking two bounded open sets A, B and producing a new open set A ⊕ B. We prove that, up to sets of measure zero, there is only one such sum satisfying a natural list of axioms. It is the scaling limit of the Diaconis–Fulton smash sum.