 The diagram is intended to indicate that all Bernoulli systems are Kolmogorov systems, all Kolmogorov systems are strong mixing systems, and so on. Hence all systems in EH are ergodic. However, the converse relations do not hold: not all ergodic systems are weak mixing, and so on. In what follows a system that is ergodic but not weak mixing is referred to as merely ergodic and similarly for the next three  levels.[8] 