Descriptive set theory was essentially born in 1917 because Souslin noticed a mistake in a 1905 paper of Lebesgue. To be more precise Lebesgue "proved" that the projection to $\mathbb R$ of a Borel set in $\mathbb R^2$ is Borel (his mistake was in assuming that decreasing countable intersections commute with projections).

It's hard to guess exactly what would have happened if Lebesgue had noticed this issue himself, but the whole field of descriptive set theory could have developed in a different way from the one we know

Descriptive set theory was essentially born in 1917 because Souslin noticed a mistake in a 1905 paper of Lebesgue. To be more precise Lebesgue "proved" that the projection to $\mathbb R$ of a Borel set in $\mathbb R^2$ is Borel (his mistake was in assuming that decreasing countable intersections commute with projections).

It's hard to guess exactly what would have happened if Lebesgue had noticed this issue himself, but the whole field of descriptive set theory could have developed in a different way from the one we know.