ɪn fˈækt, wˌaɪl hiː wʌzɐ ɹᵻsˈɜːtʃ stˈuːdənt ʌv nˈɪkəlˌaɪ lˈuːzɪn ɪn nˈaɪntiːnhˈʌndɹɪd sˈɛvəntˌiːn hiː fˈaʊnd ɐn ˈɛɹɚɹ ɪn ɐn ˈɑːɹɡjuːmənt ʌv lˈɛbɛsɡ, hˌuː bᵻlˈiːvd hiː hæd pɹˈuːvd ðæt fɔːɹ ˌɛni bˈɔːɹəl sˈɛt ˈɪn , ðə pɹədʒˈɛkʃən ˌɑːntʊ ðə ɹˈiːəl ˈæksɪs wʌz ˈɔːlsoʊ ɐ bˈɔːɹəl sˈɛt.
In fact, while he was a research student of Nikolai Luzin (in 1917) he found an error in an argument of Lebesgue, who believed he had proved that for any Borel set in , the projection onto the real axis was also a Borel set.