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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.01190 |
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Table of Contents:
- We prove that if $A,B$ are compact subsets of $\mathbb{R}$ such that the upper density of $B$ is positive at every point of $B$, then there is a closed null set $N\subset A$ such that $N+B=A+B$. As a corollary we find that if $A,B\subset \mathbb{R}$ are measurable, and every null subset $N$ of $A$ can be translated into $B$ (that is, if $B$ contains a suitable translate of $N$), then there is a null set $N_0$ such that $A\setminus N_0$ can be translated into $B$. The topic is related to some consistency results of the theory of additive properties of the reals.