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We obtain a far-reaching generalization (in several directions) of thetheorem of A. Lambert on the existence of the projective tensor product ofoperator sequence spaces. This result is obtained in the context of spaces,generalizing $p$-multinormed spaces of Dales et al. which are based on anarbitrary, perhaps non-discrete measure.

The existence of $p$-convex tensor products of $L_p(X)$-spaces for the case of an arbitrary measure