Here $F$ is assumed to be open. [ But: We assume that $F$ is open, not: “We assume $F$ to be open”.]
......, the limit being assumed to exist for every real $x$.
The assumed positivity of $u_n$ is essential for these results.
We can assume, by decreasing $n$ if necessary, that ......
We may (and do) assume that ......
We tacitly assume that ......
It is assumed that ......
We follow Kato [3] in assuming that $f$ is upper semicontinuous.
The reader is assumed to be familiar with elementary $K$-theory.
Then $X$ assumes values $0,1,...,9$, each with probability $1/10$.
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