Null Measurability at the Symmetrization Interface in VC Learning
Recent work revisiting measurability in the fundamental theorem of statistical learning imposes Borel measurability of ghost-gap suprema. We show that, at the one-sided ghost-gap interface actually used by the standard symmetrization proof, this requirement is stronger than necessary. For any Borel-parameterized concept class on a Polish domain, the bad event "there exists a hypothesis whose ghost empirical error exceeds its training empirical error by at least ε/2" is analytic. By Choquet capacitability, it is therefore measurable in the completion of every finite Borel measure. We then construct a concept class whose bad event is null-measurable but not Borel, giving a strict separation...
| Authors | Dhruv Gupta |
|---|---|
| Primary category | cs.LG |
| Published | 27 April 2026 |
| Last updated at source | 27 April 2026 |
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