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Dynkin's π-λ Theorem states that if $\mathcal{P}$ is a π-system and $\mathcal{D}$ is a λ-system containing $\mathcal{P}$, then $\mathcal{D}$ contains the σ-algebra generated by $\mathcal{P}$. This theorem is a powerful tool in proving the equality of measures.

The concept of monotone classes relates to Dynkin's π-λ Theorem in that every λ-system is a monotone class, but the converse is not necessarily true. A monotone class is a collection of subsets closed under countable increasing unions or intersections and decreasing intersections. This connection is pivotal in constructing measures and understanding convergence.

A λ-system, also known as a Dynkin system, is a collection of subsets of a set that contains the universal set, is closed under complementation, and is closed under countable disjoint union. Dynkin's π-λ Theorem characterizes λ-systems in relation to π-systems.

A π-system is a collection of subsets of a set that is closed under finite intersection. Dynkin's π-λ Theorem relies on a π-system as a starting point for the application of the theorem.