[see also: ensure]

Observe how the completeness of $L^2$ was used to guarantee the existence of $f$.

However, (5) is sufficient to guarantee invertibility in $A$.

We are guaranteed only one dense product for each $k$.

This guarantees that $f$ satisfies all our requirements.

......, which, by another theorem of Kimney's, is more than enough to guarantee that $P$ gives $A$ outer measure 1.

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