[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 $f(0)\neq 0$ causes no harm in applications, for if ......
Assume, in addition to the hypotheses of Exercise 4, that ......
We now bound $v$ on $\langle$under$\rangle$ the hypothesis $H_m$.
In fact, we shall prove our result under the weaker hypothesis that $W$ is weakly bounded, rather than just bounded, on an infinite subset of $G$.
However, a slight strengthening of the hypotheses does give us a regular measure.
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
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