[see also: condition, hypothesis, requirement]
We make two standing assumptions on the maps under consideration.
By the smoothness assumption on $f$, ......
By assumption, ......
If the boundary is never hit then $x_t$ is a Feller process under reasonable continuity assumptions.
We establish our results both unconditionally and on the assumption of the Riemann Hypothesis.
We note that the assumption of GCH is made for convenience and ease of presentation.
Then $F$ is continuous at zero, contrary to assumption.
a basic $\langle$fundamental/implicit/tacit/underlying/reasonable/erroneous$\rangle$ assumption
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