Ulam’s Conjecture

Abstract

The conjecture of Ulam states that the standard product probability measure π on the Hilbert cube Iω is invariant under the induced metric da when the sequence a={ai}i∈ℕ of positive numbers satisfies condition (4.1 ). This conjecture was proved in [6] when E1 is a non-degenerate subset of Ma. In this chapter, we will completely prove Ulam’s conjecture to be true by considering both non-degenerate as well as degenerate cases. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.