Lebesgue

Monotone Convergence Theorem

• The Monotone Convergence Theorem (MCT) allows interchange of limit and integral for increasing nonnegative functions. • MCT requires pointwise a.e. convergence, measurability, an

Dominated Convergence Theorem

• DCT states limit and integral commute under pointwise a.e. convergence with integrable dominating function. • Requires measurable functions and existence of integrable g bounding