Question: what is inner and outer measure?
Answer: Induced inner measures are often used in combination with outer measures to extend a measure to a larger σ-algebra. If μ is a finite measure defined on a σ-algebra Σ over X and μ* and μ* are corresponding induced outer and inner measures, then the sets T ∈ 2X such that μ*(T) = μ* (T) form a σ-algebra with .