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Of course, it seems the answer is obviously "hypothesis". However, that translation does not seem right in the following context, taken from a paper by Bernard Host.

Désormais, $p > 1$ est un entier et $\mu$ une mesure de probabilité sur $\mathbb{T}$; on ne fait pour l'instant aucune hypothèse d'invariance.

Using Google Translate, my best translation is the following.

Henceforth, let $p>1$ be an integer and let $\mu$ be a probability measure on $\mathbb{T}$; As of yet we do not have an invariance hypothesis."

But isn't a hypothesis the same as a conjecture (e.g. Riemann hypothesis)? "Conjecture" doesn't seem to fit here. My gut tells me that the last part should read "As of yet we do not make any assumption about invariance." So, in this context, does "hypothèsis" mean "assumption"?

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    $\begingroup$ hypothèse is the same as assumption $\endgroup$ – Gabriel Romon Sep 1 '16 at 16:07
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    $\begingroup$ @John: English hypothesis can mean ‘conjecture’, but it can also mean ‘assumption’: we speak of the hypotheses of a given theorem, meaning the assumptions. However, I would translate the second clause as for now we do not assume invariance. $\endgroup$ – Brian M. Scott Sep 1 '16 at 16:18
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    $\begingroup$ The normal meaning, in English as well as in French is one of the meanings of the Greek word ̔υπόθεσις : supposition. $\endgroup$ – Bernard Sep 1 '16 at 18:25
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"Hypothesis" does not mean conjecture.

Suppose I say "Let $P$ be a probability measure on $\mathbb R^2$ that is invariant under rotations about the origin. Then we can conclude that..."

Then rotation-invariance is a hypothesis. That $P$ is a probability measure is a hypothesis.

Theorems typically have hypotheses and conclusions.

Thus "hypothesis" seems like a reasonable translation.

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