[ pl. hypotheses; see also: assumption, conjecture]
We show that one can drop an important hypothesis of the saddle point theorem without affecting the result.
The hypothesis f(0)≠ 0 causes no harm in applications, for if......
Assume, in addition to the hypotheses of Exercise 4, that......
We now bound v on <under> the hypothesis Hm.
We establish our results both unconditionally and on the assumption of the Riemann Hypothesis.
In geometric language, the hypothesis is that F is......; part of the conclusion is that F satisfies......
the hypothesis of positivity [= the positivity hypothesis]
the hypothesis of F being projective\vadjust{\eject}