no. 4
The return time theorem fails on infinite measure-preserving systems
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 4, pp. 491-495 
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     author = {Lacey, Michael T.},
     title = {The return time theorem fails on infinite measure-preserving systems},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {491--495},
     year = {1997},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {4},
     mrnumber = {1465799},
     zbl = {0894.60001},
     language = {en},
     url = {https://www.numdam.org/item/AIHPB_1997__33_4_491_0/}
}
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Lacey, Michael T. The return time theorem fails on infinite measure-preserving systems. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 4, pp. 491-495. https://www.numdam.org/item/AIHPB_1997__33_4_491_0/

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