Integration Theory

When to Use

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

Decision Tree

1. Simple function integration

   • For s = sum(a_i * chi_{E_i}): integral s dmu = sum(a_i * mu(E_i))
   • sympy_compute.py simplify "simple_integral"

2. Monotone Convergence Theorem (MCT)

   • If 0 <= f_n <= f_{n+1} and f_n -> f:
   • lim integral(f_n) = integral(lim f_n)
   • Use for increasing sequences

3. Dominated Convergence Theorem (DCT)