History of Ulam’s Conjecture

Abstract

A conjecture of Ulam states that the standard product probability measure π on the Hilbert cube Iω is da-invariant when the sequence a={ai}i∈ℕ of positive numbers satisfies the condition ∑i=1∞ai2<∞. In 1974 and 1977, J. Mycielski published the first papers on this topic. Indeed, he proved the conjecture of Ulam affirmatively under the additional assumption that the sets are open. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.