Definition:Stratified Random Sample

Definition
Let $P$ be a population.

Let $S \subsetneq P$ be a sample.

Let be a, where each $P_i$ is defined by a certain property.

Then $S$ is a stratified random sample iff:


 * There exists a finite expansion $P = P_1 \mid P_2 \mid \cdots \mid P_k$ of $P$ such that $S$ is the union of $k$ simple random samples, one taken from each $P_i$.

Note on terminology
The components of $P$ are called strata, singular stratum.