due

Observe that $A$ is a vector space. This is due to two facts: ......

We have $F=G=H$, the last equality being due to the fact that ......

Theorems 1 to 3 are classical results, due to Lebesgue.

This proof is due to R. P. Boas.

[In the above examples, due is an adjective; the use of `due to' as a preposition meaning `because of', e.g. “Due to Theorem 5, this map is bounded”, although quite common, is considered incorrect by some native speakers of English.]



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