[see also: assumption, requirement
We prove, under mild conditions on f, that......
In this section we investigate under what conditions the converse holds.
They established the Hasse principle subject to a rank condition on the coefficients.
This is a condition on how large f is.
The next theorem provides conditions for the existence of......
The corollary gives a necessary and sufficient condition on p for g to belong to Ap.
A necessary and sufficient condition for A to be open is that C be closed.
This condition also turns out to be necessary.
When the rank condition fails we use (3) instead.
Condition (c) is intended to give us firm control over......
We note that H is in fact not Lipschitz continuous if this condition is violated.
We first check that t' obeys the condition for f(t).
It should be no surprise that a condition like ai≠ bi turns up [= appears, shows up] in this theorem.
a restrictive <stringent> condition