Lebesgue Measure

When to Use

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

Decision Tree

1. Outer measure construction

   • m*(A) = inf{sum |I_n| : A subset union(I_n)}
   • sympy_compute.py sum "length(I_n)" --var n

2. Caratheodory criterion

   • E is measurable if: m*(A) = m*(A & E) + m*(A & E^c) for all A
   • z3_solve.py prove "caratheodory_criterion"

3. Lebesgue measure properties

   • Translation invariant: m(E + x) = m(E)