Apakah ada versi berkelanjutan dari teorema pengulangan paralel
Raz Paralel pretition teorema adalah hasil yang penting dalam PCP, inapproximation, dll Teorema ini fomalized sebagai berikut. G=(S,T,A,B,π,V)G=(S,T,A,B,π,V)G=(\mathcal{S},\mathcal{T},\mathcal{A},\mathcal{B},\pi, V)S,T,A,BS,T,A,B\mathcal{S},\mathcal{T},\mathcal{A},\mathcal{B}ππ\piS×TS×T\mathcal{S}\times\mathcal{T}V:S×T×A×B→{0,1}V:S×T×A×B→{0,1}V:\mathcal{S}\times\mathcal{T}\times\mathcal{A}\times\mathcal{B}\rightarrow\{0,1\}v(G)=maxhA∈HA,hB∈HB∑s,tπ(s,t)V(s,t,hA(s),hB(t))v(G)=maxhA∈HA,hB∈HB∑s,tπ(s,t)V(s,t,hA(s),hB(t))v(G)=\max_{h_A\in\mathcal{H}_A,h_B\in\mathcal{H}_B}\sum_{s,t}\pi(s,t)V(s,t,h_A(s),h_B(t)) And nnn-fold game Gn=(Sn,Tn,An,Bn,πn,Vn)Gn=(Sn,Tn,An,Bn,πn,Vn)G^n=(\mathcal{S}^n,\mathcal{T}^n,\mathcal{A}^n,\mathcal{B}^n,\pi^n, V^n). The theorem says if v(G)≤1−ϵ,v(G)≤1−ϵ,v(G)\leq 1-\epsilon, then v(Gn)≤(1−ϵc)Ω(nlogmax{|A|,|B|})v(Gn)≤(1−ϵc)Ω(nlogmax{|A|,|B|})v(G^n)\leq (1-\epsilon^c)^{\Omega(\frac{n}{\log\max\{|A|,|B|\}})}. My quesion is what happen if the sets are infinite, in a continuous space. Say if S,T,A,BS,T,A,B\mathcal{S},\mathcal{T},\mathcal{A},\mathcal{B} …