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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.

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.

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.

Dynkin's π-λ Theorem is used in probability and measure theory to demonstrate the equality of measures and to extend measures from a π-system to a σ-algebra. It is a crucial step in the proof of important results such as the uniqueness of extension of probability measures.