The σ-algebra of τ-past, (also named stopped σ-algebra, stopped σ-field, or σ-field of τ-past) is a σ-algebra associated with a stopping time in the theory of stochastic processes, a branch of probability theory.
Let be a stopping time on the filtered probability space . Then the σ-algebra
is called the σ-algebra of τ-past.
Is are two stopping times and
almost surely, then
A stopping time is always -measurable