#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## follow

[*see also*: imply, ensuing, subsequent

The remarks following Theorem 2 show that a=0.

The analysis to follow only covers the case d=1.

The following three statements are equivalent:......

For D a smooth domain, the following are equivalent.

The idea of the ensuing computations is the following:......

His argument is as follows.

The fact that the number T(p) is uniquely defined, even though p is not, enables us to define the nullity of A as follows.

In what follows <In all that follows>, L stands for......

Throughout what follows, we shall freely use without
explicit mention the elementary fact that......

It follows that a is positive. [= Hence <Consequently,/Therefore,>
a is positive.]

If we prove that G>0, the assertion follows.

The general case follows by changing x to x-a.

We follow Kato [3] in assuming f to be upper semicontinuous.

The proof follows very closely the proof of (2), except for the appearance
of the factor x^{2}.

It is intuitively clear that the amount by which S_{n} exceeds zero
should follow the exponential distribution.

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