Proof of Theorem 4.3
Laurent Fribourg, Romain Soulat · 2013
Proof of Theorem 4.3Consider a k-invariant decomposition Δ = {(V i , π i )} i∈I of R, and the sequence {R j Δ } j≥0 and its limit R * Δ defined in Chapter 4.Let us consider the (compact) convex sets W k σ where k ∈ N and σ ∈ I k , defined as follows:-W 0 = R where denotes the empty sequence.-W k+1(i•σ) = Post π i (W k σ ∩V i ) with i ∈ I and σ ∈ I k .It is easy to show that, for all k ∈ N and all σ ∈ I k , W k σ is a compact convex set such that: