Analytic Continuation

When Ω₁,Ω₂ are two regions such that and, i = 1, 2, while f₁(z) = f₂(z) in Ω₃ then the function element (f₂, Ω₂) resp. (f₁, Ω₁) is an immediate analytic continuation of the function element (f₁, Ω₁) resp. (f₂,Ω₂). When Ω _i , 1 ≤ i ≤n, is a finite sequence of regions such that $$ \Omega _i \cap \Omega _{i + 1} \ne \not 0,1 \leqslant i \leqslant n - 1,\,f_i \in H(\Omega _i ),1 \leqslant i \leqslant n $$, and each (f _i+1, Ω _i+1) is an immediate analytic continuation of (f _i , Ω _i ) then (f _n , Ω _n ) is an analytic continuation of (f₁, Ω₁).