#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## condition

[*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 A_{p}.

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 a_{i}≠ b_{i} turns up
[= appears, shows up] in this theorem.

a restrictive <stringent> condition

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