The modified, discrete Lévy transformation is Bernoulli
Séminaire de probabilités de Strasbourg, Tome 26 (1992), pp. 157-161. 
@article{SPS_1992__26__157_0,
     author = {Dubins, Lester E. and Smorodinsky, Meir},
     title = {The modified, discrete {L\'evy} transformation is {Bernoulli}},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     pages = {157--161},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {26},
     year = {1992},
     mrnumber = {1231991},
     zbl = {0761.60043},
     language = {en},
     url = {http://archive.numdam.org/item/SPS_1992__26__157_0/}
}
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Dubins, Lester E.; Smorodinsky, Meir. The modified, discrete Lévy transformation is Bernoulli. Séminaire de probabilités de Strasbourg, Tome 26 (1992), pp. 157-161. http://archive.numdam.org/item/SPS_1992__26__157_0/

Doob, J.L., 1953. Stochastic Processes. John Wiley & Sons, Inc., New York. | Zbl

Levy, Paul, 1939. Sur certains processus stochastiques homogenes. Compositio Mathematica 7, 283-339. | JFM | Numdam | MR | Zbl

Levy, Paul, 1948. Processus Stochastiques et Mouvement Brownien. Gauthier-Villars. | MR | Zbl

Kuratowski, K. 1966. Topology. Academic Press, New York and London. | MR | Zbl

Ornstein, Donald, 1974. Ergodic Theory, Randomness, and Dynamical Systems. Yale University Press. | MR | Zbl

Sinai, Ya.G. 1962. A Weak Isomorphism of Transformations Having an Invariant Measure. Dokl.Akad.Nauk. SSSR 147, 797-800. | MR | Zbl