measurable space

Definition

A measurable space is a pair $(Y, \mathcal{F})$, with $Y$ denoting a set, and $\mathcal{F}$ a σ-algebra over $Y$.

Notes

• the concepts of a measurable space and topological space are similar in that both contain the set $X$ and $\emptyset$, but the topology is closed under arbitrary unions and finite intersections, rather than countable unions, countable intersections, and complements
  • (also see Borel σ-algebra)
• if equipped with a measure, it is a measure space

References

1. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, p. 344.
2. https://ncatlab.org/nlab/show/measurable+space
3. https://math.stackexchange.com/questions/1330649/difference-between-topology-and-sigma-algebra-axioms