Is a measurable set still measurable when projected to lower dimensions?
Lebesgue initially believed this in 1905, but Souslin discovered it to be false while studying Lebesgue's results for his thesis. This led to the development of the theory of Souslin spaces, which despite being relatively unknown, is valuable in connecting measures and topologies. One application is to determine if a measure gives mass to compact sets in any topology of a space. We will present this question and explore when the answer could be affirmative, which was a breakthrough of my thesis on optimal transport.
No special background knowledge is required as the question concerns only basic concepts of topology and measure, and the talk will focus on core ideas. For detailed proofs, refer to my blog on Souslin spaces: https://jingmatrix.github.io/en/writing/2022-09-29-Compactness-from-Souslin-Spaces