Sigma Algebras

When to Use

Use this skill when working on sigma-algebras problems in measure theory.

Decision Tree

1. Verify sigma-algebra axioms

   • X in F (whole space is measurable)
   • A in F implies A^c in F (closed under complements)
   • A_n in F implies union(A_n) in F (closed under countable unions)
   • z3_solve.py prove "sigma_algebra_axioms"

2. sigma-algebra generation

   • Start with generating collection C
   • sigma(C) = smallest sigma-algebra containing C
   • Use Dynkin's pi-lambda theorem for uniqueness