Almost all sets of nonnegative integers and their small perturbations are not sumsets
نویسندگان
چکیده
Fix α ∈ ( 0 , 1 / 3 stretchy="false">) \alpha \in (0,1/3) . We show that, from a topological point of view, almost all sets alttext="upper A subset-of-or-equal-to double-struck upper N"> A ⊆<!-- ⊆ <mml:mi mathvariant="double-struck">N encoding="application/x-tex">A\subseteq \mathbb {N} have the property if prime equals A"> class="MJX-variant" mathvariant="normal">′<!-- ′ </mml:msup> = encoding="application/x-tex">A^\prime =A for but alttext="o n Superscript alpha Baseline o n encoding="application/x-tex">o(n^{\alpha }) elements, then prime"> encoding="application/x-tex">A^\prime is not nontrivial sumset B plus C"> B + C encoding="application/x-tex">B+C In particular, encoding="application/x-tex">A are totally irreducible. addition, we prove that measure analogue holds with 1"> =1
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2023
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/proc/16392