##  [Measure Space](/measure-space) 

  ##  [Measure Space](https://natural.quantumdictionary.io/measure-space-0) 

  

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**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](https://mathlogic.quantumdictionary.io/measure-space-1) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- 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](https://puremath.quantumdictionary.io/measure-space-2) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- 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.