He did not, however, immediately demonstrate the equivalence of his own definition to that of Lebesgue, and this later led to some controversy with other mathematicians.
Siya ay hindi, gayunman, agad-agad na ipakita ang pagkapareho ng kanyang sariling kahulugan sa na ng Lebesgue, at ito mamaya na humantong sa ilang mga alitan sa iba pang mga mathematicians.