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Monografiya posvyashhena detal'nomu izlozheniju osobennostej vypolneniya statisticheskih jergodicheskih teorem (SJeT) dlya perestanovochno-invariantnyh (simmetrichnyh) prostranstv izmerimyh funkcij, zadannyh na prostranstve Lebega s konechnoj ili sigma-konechnoj nepreryvnoj meroj. Rassmotreny sluchai diskretnogo (avtomorfizmy) i nepreryvnogo (potoki) vremeni. V sluchae, esli mera konechna, pokazano, chto SJeT verny v separabel'nyh simmetrichnyh prostranstvah i tol'ko v nih, a dlya neseparabel'nyh simmetrichnyh prostranstv vydelyaetsya separabel'noe podprostranstvo - zamykanie mnozhestva ogranichennyh funkcij v SP, dlya jelementov kotorogo SJeT verny. V sluchae beskonechnoj mery ustanovleno, chto SJeT verny togda i tol'ko togda, kogda simmetrichnoe prostranstvo separabel'no i ne soderzhitsya v prostranstve integriruemyh funkcij.