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If      ( M 1 , τ  1 ) (M_{1},\tau _{1})       is a finite von Neumann algebra and if      ( M 2 , τ  2 ) (M_{2},\tau _{2})       is an infinite (semifinite) von Neumann algebra, then      L p ( M 1 , τ  1 ) L_{p}(M_{1},\tau _{1})       and      L p ( M 2 , τ  2 ) L_{p}(M_{2},\tau _{2})       are non-isomorphic for all      p ∈  ( 1 , ∞  ) , p ≠  2 p\in (1,\infty ), p\neq 2       .

Non-isomorphism of 𝐿_{𝑝}-spaces associated with finite and infinite von Neumann algebras