Measure Theory glossary
Clear, one-line definitions of the Measure Theory terms used across the OgbonLab textbooks. Each entry links to the interactive sections where the idea is taught.
8 terms
- borel sigma-algebra
- The smallest σ-algebra on a topological space containing all open sets; its members are the Borel sets.
- cantor set
- The closed subset of [0,1] obtained by iteratively removing middle thirds; uncountable, measure zero, and totally disconnected.
- See: Sets of Measure Zero and the Cantor Set
- lebesgue measure
- The unique translation-invariant measure on ℝⁿ assigning volume b - a to each interval [a, b]; extends length, area, and volume.
- See: Sigma-Algebras and Lebesgue Measure
- measurable function
- A function f: X → Y between measurable spaces with f⁻¹(B) measurable for every measurable B; the natural domain of integration.
- null set
- A measurable set of measure zero; properties holding outside a null set are said to hold almost everywhere.
- probability measure
- A measure μ on a σ-algebra with μ(X) = 1; assigns probabilities to events while satisfying countable additivity.
- sigma-algebra
- A collection of subsets of X closed under complements and countable unions, containing ∅; the natural domain for a measure.
- See: Sigma-Algebras and Lebesgue Measure
- simple function
- A measurable function taking only finitely many values; finite linear combinations of indicator functions used to build the Lebesgue integral.