Borel reducibility and finitely Holder(α) embeddability

Original · EN

Let (Xₙ,dₙ),n∈ N be a sequence of pseudo-metric spaces, p≥ 1. For x,y∈∏n∈ NXₙ, let (x,y)∈ E((Xₙ)n∈ N;p)∑n∈ Ndₙ(x(n),y(n))ᵖ<+∞. For Borel reducibility between equivalence relations E((Xₙ)n∈ N;p), we show it is closely related to finitely Hölder(α) embeddability between pseudo-metric spaces.