Measure Space
Natural & Formal Sciences Dictionary
Definition
A triple (X, Σ, μ) where X is a set, Σ is a σ-algebra of subsets of X, and μ is a measure assigning a nonnegative extended real number to each set in Σ, satisfying μ(∅)=0 and countable additivity.
Measure Space
- Natural & Formal Sciences -
Mathematics & Logic Dictionary
Definition
A triple (X, Σ, μ) where X is a set, Σ is a σ-algebra of subsets of X, and μ: Σ → [0,∞] is a countably additive function (measure) assigning extended nonnegative real values to measurable sets, with μ(∅)=0.
Measure Space
- Mathematics & Logic -
Pure Mathematics Dictionary
Definition
A triple (X, Σ, μ) where X is a set, Σ is a sigma-algebra of subsets of X, and μ: Σ → [0,∞] is a countably additive measure defined on Σ.