Geodesic
Minimal Self-Joinings of Infinite Mixing Actions of Rank~1
Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 851-856

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We prove that measure-preserving actions of rank 1 of the groups $\mathbb{Z}^n$ and $\mathbb{R}^n$ on a Lebesgue space with a $\sigma$-finite measure have minimal self-joinings.
Keywords: space with a $\sigma$-finite measure, measure-preserving transformation, action of rank 1, minimal self-joining. 
@article{MZM_2017_102_6_a5,
     author = {I. V. Klimov and V. V. Ryzhikov},
     title = {Minimal {Self-Joinings} of {Infinite} {Mixing} {Actions} of {Rank~1}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {851--856},
     publisher = {mathdoc},
     volume = {102},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a5/}
}
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I. V. Klimov; V. V. Ryzhikov. Minimal Self-Joinings of Infinite Mixing Actions of Rank~1. Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 851-856. http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a5/