Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying th

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by

This groundbreaking volume is the first to elaborate the theory of set families as a tool for studying the phenomenon of recurrence. The theory is implicit in s

Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the t

Nilsystems play a key role in the structure theory of measure preserving systems, arising as the natural objects that describe the behavior of multiple ergodic