---
type: Fractal Concept
title: Hausdorff Dimension
description: Rigorous notion of dimension defined as the infimum of d such that the d-dimensional Hausdorff measure of the set is zero.
resource: https://tyson-swetnam.github.io/fractal-notebooks/okf/concepts/dimension-theory/hausdorff-dimension/
tags:
- dimension-theory
- measure-theory
aliases:
- hausdorff-besicovitch dimension
- hausdorff measure
sources:
- id: glossary
  resource: https://tyson-swetnam.github.io/fractal-notebooks/foundations/glossary/
  title: Fractal Notebooks glossary (Chapter 4)
- id: seed
  resource: https://github.com/tyson-swetnam/fractal-notebooks/blob/main/fractal_rag/src/fractal_rag/concepts/seed.yaml
  title: fractal_rag concept seed (seed.yaml)
generated:
  by: process:fractal-rag-okf-export
  at: "2026-10-24T00:00:00Z"
status: stable
---

# Definition

Rigorous notion of dimension defined as the infimum of d such that the d-dimensional Hausdorff measure of the set is zero.

# Aliases

`hausdorff-besicovitch dimension`, `hausdorff measure`

# Citations

[1] [Fractal Notebooks glossary (Chapter 4)](https://tyson-swetnam.github.io/fractal-notebooks/foundations/glossary/) — `docs/foundations/glossary.md`

[2] [fractal_rag concept seed (seed.yaml)](https://github.com/tyson-swetnam/fractal-notebooks/blob/main/fractal_rag/src/fractal_rag/concepts/seed.yaml) — `fractal_rag/src/fractal_rag/concepts/seed.yaml`