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://www.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://www.numdam.org/item/SPS_1992__26__157_0/

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