Measure Theory (07/15) - The sigma-algebra generated by a collection of subsets (1/2)
From Joel Feinstein
Audio narration (with digital pointer) to go with Slide 37 of G14FTA where the original recording failed.
Brief discussion of how to generate a topology from a collection of sets (as a sub-base), and how it is harder to give such a concrete approach to generating a σ-algebra. The intersection of any family of σ-algebras on X is still a σ-algebra on X. The definition of the σ-algebra on a set X generated by a collection of subsets of X. Brief discussion relating this to open sets and sets with the Property of Baire.
For more information and links to further resources, see my blog page