Simple proofs of discretised projection theorems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915639551066112 |
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| author | O'Regan, William Shmerkin, Pablo Wang, Hong |
| author_facet | O'Regan, William Shmerkin, Pablo Wang, Hong |
| contents | We give a simple, short and self-contained presentation of Bourgain's discretised projection theorem from 2010, which is a fundamental tool in many recent breakthroughs in geometric measure theory, harmonic analysis, and homogeneous dynamics. Our main innovation is a short elementary argument that shows that a discretised subset of $\R$ satisfying a weak ``two-ends'' spacing condition is expanded by a polynomial to a set of positive Lebesgue measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple proofs of discretised projection theorems O'Regan, William Shmerkin, Pablo Wang, Hong Classical Analysis and ODEs Combinatorics Metric Geometry 11B30, 28A75, 28A80 We give a simple, short and self-contained presentation of Bourgain's discretised projection theorem from 2010, which is a fundamental tool in many recent breakthroughs in geometric measure theory, harmonic analysis, and homogeneous dynamics. Our main innovation is a short elementary argument that shows that a discretised subset of $\R$ satisfying a weak ``two-ends'' spacing condition is expanded by a polynomial to a set of positive Lebesgue measure. |
| title | Simple proofs of discretised projection theorems |
| topic | Classical Analysis and ODEs Combinatorics Metric Geometry 11B30, 28A75, 28A80 |
| url | https://arxiv.org/abs/2511.21656 |