caa a22 4500 469068728 CHVBK 20180323132915.0 cr unu---uuuuu 170328e19920601xx s 000 0 eng 10.1007/BF02808154 doi (NATIONALLICENCE)springer-10.1007/BF02808154 King Jonathan Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA aut Ergodic properties where order 4 implies infinite order [Elektronische Daten] [Jonathan King] For a family of dynamical properties, knowing that the condition holds for order 4 implies that it holds for all orders. Here we establish this for the properties minimal self-joinings, simplicity and for cartesiandisjointness. An application of the first yields an analog to Kalikow's celebrated result that for rank-1 transformations, 2-fold mixing implies 3-fold mixing. Via a joining argument we show that for any rank-1 ℤ D -action, 4-fold mixing implies mixing of all orders. Indeed, the rank need only be sufficiently close to 1 for the implication to hold and so this result is new even when the acting group is ℤ. By means of limit-joinings, we settle affirmatively an old open question by establishing, for anyM, thatM-fold Rényi-mixing impliesM-fold mixing. Hebrew University, 1992 Israel Journal of Mathematics Springer-Verlag 80/1-2(1992-06-01), 65-86 0021-2172 80:1-2<65 1992 80 11856 https://doi.org/10.1007/BF02808154 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02808154 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- King Jonathan Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 80/1-2(1992-06-01), 65-86 0021-2172 80:1-2<65 1992 80 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer