  The existence of the {\em typical set} is key for data compression strategies
and for the emergence of robust statistical observables in macroscopic physical
systems. Standard approaches derive its existence from a restricted set of
dynamical constraints. However, given the enormous consequences for the
understanding of the system's dynamics, and its role underlying the presence of
stable, almost deterministic statistical patterns, a question arises whether
typical sets exist in much more general scenarios. We demonstrate here that the
typical set can be defined and characterized from general forms of entropy for
a much wider class of stochastic processes than it was previously thought. This
includes processes showing arbitrary path dependence, long range correlations
or dynamic sampling spaces; suggesting that typicality is a generic property of
stochastic processes, regardless of their complexity. Our results impact
directly in the understanding of the stability of complex systems, open the
door to new data compression strategies and points to the existence of
statistical mechanics-like approaches to systems arbitrarily away from
equilibrium with dynamic phase spaces. We argue that the potential emergence of
robust properties in complex stochastic systems provided by the existence of
typical sets has special relevance to biological systems.
