Separable sigma algebra

In mathematics, s-algebras are usually studied in the context of measure theory. A separable s-algebra (or separable s-field) is a s-algebra which is a separable space when considered as a metric space with metric  for and a given measure  (and with being the symmetric difference operator). Note that any s-algebra generated by a countable collection of sets is separable, but the converse need not hold. For example, the Lebesgue s-algebra is separable (since every Lebesgue measurable set is equivalent to some Borel set) but not countably generated (since its cardinality is higher than continuum).