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},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {4},
     year = {1997},
     mrnumber = {1465799},
     zbl = {0894.60001},
     language = {en},
     url = {http://archive.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. http://archive.numdam.org/item/AIHPB_1997__33_4_491_0/

[AD] J. Aaronson and M. Denker, On the FLIL for certain ψ-mixing processes and infinite measure-preserving transformations, (English. French summary), C. R. Acad. Sci. Paris, Série I, Math., Vol. 313, 1991, pp. 471-475. | MR | Zbl

[BL] A. Bellow and V. Losert, The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences, Trans. Amer. Math. Soc., Vol. 288, 1985, pp. 307-345. | MR | Zbl

[B] J. Bourgain, Almost sure convergence and bounded entropy, Israel J. Math., Vol. 63, 1988, pp. 79-97. | MR | Zbl

[BFKO] J. Bourgain, H. Furstenberg, Y. Katznelson and D. Ornstein, Return times of dynamical systems, Appendix to : Pointwise ergodic theorems for arithmetic sets, by J. Bourgain, Pub. Math. I.H.E.S., Vol. 69, 1989, pp. 5-45. | EuDML | Numdam | MR | Zbl

[D] R.M. Dudley, Real Analysis and Probability, Wadsworth & Brooks/Cole, Pacific Grove, Gal., 1989. | Zbl

[LPRW] M. Lacey, K. Petersen, D. Rudolph and M. Wierdl, Random ergodic theorems with universally representative sequences, Ann. Instit. H. Poincaré, Vol. 30, 1994, pp. 353-395. | EuDML | Numdam | MR | Zbl

[W] M. Wichura, Functional law of the iterated logarithm for the partial sums of i.i.d. random variables in the domain of attraction of a completely asymmetric stable law, Ann. Probab., Vol. 2, 1974, pp. 1108-1138. | MR | Zbl

[WW] N. Wiener and A. Wintner, Harmonic analysis and ergodic theory, Amer. J. Math., Vol. 63, 1941, pp. 415-426. | JFM | MR | Zbl