Any free Borel flow is shown to admit a cross section with only two possible distances between adjacent points, answering an old question of Nadkarni. As an application of this result, we derive a short proof of the classification of Borel flows up to Lebesgue orbit equivalence.
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Konstantin Slutsky, Regular cross sections of Borel flows. J. Eur. Math. Soc. 21 (2019), no. 7, pp. 1985–2050DOI 10.4171/JEMS/879