# On the Vapnik-Chervonenkis dimension of products of intervals in ℝd

arXiv: https://arxiv.org/abs/2104.07136 · HTML: https://mlsanity.com/paper/2104.07136/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 10 references that are in the map.
- First posted on arXiv 14 Apr 2021.

## Builds on (most cited first, 1 of 1)

- [Elementos da teoria de aprendizagem de m'aquina supervisionada](https://mlsanity.com/paper/1910.06820/) (2019)

## Abstract (arXiv)

We study combinatorial complexity of certain classes of products of intervals in ℝd, from the point of view of Vapnik-Chervonenkis geometry. As a consequence of the obtained results, we conclude that the Vapnik-Chervonenkis dimension of the set of balls in ℓ_∞d -- which denotes Rd equipped with the sup norm -- equals lfloor (3d+1)/2rfloor.