Given $$\sigma $$ σ -finite measure spaces $$(\Omega _1,\Sigma _1, \mu _1)$$ ( Ω 1 , Σ 1 , μ 1 ) and $$(\Omega _2,\Sigma _2,\mu _2)$$ ( Ω 2 , Σ 2 , μ 2 ) , we consider Banach spaces $$X_1(\mu _1)$$ X 1 ( μ 1 ) and $$X_2(\mu _2)$$ X 2 ( μ 2 ) , consisting of $$L^0 (\mu _1)$$ L 0 ( μ 1 ) and $$L^0 (\mu _2)$$ L 0 ( μ 2 ) measurable functions respectively, and study when the completion of the simple tensors in the projective tensor product $$X_1(\mu _1) \otimes _\pi X_2(\mu _2)$$ X 1 ( μ 1 ) ⊗ π X 2 ( μ 2 ) is continuously included in the metric space of measurable functions $$L^0(\mu _1 \otimes \mu _2)$$ L 0 ( μ 1 ⊗ μ 2 ) . In particular, we prove that the elements of the completion of the projective tensor product of $$L^p$$ L p -spaces are measurable functions with respect to the product measure. Assuming certain conditions, we finally show that given a bounded linear operator $$T:X_1(\mu _1) \otimes _\pi X_2(\mu _2) \rightarrow E$$ T : X 1 ( μ 1 ) ⊗ π X 2 ( μ 2 ) → E (where E is a Banach space), a norm can be found for T to be bounded, which is ‘minimal’ with respect to a given property (2-rectangularity). The same technique may work for the case of n-spaces.