#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## fail

[*see also*: hold, invalid

The space X fails to have the Radon-Nikodym property.

Hence A fails to satisfy (3).

For j=1 the operator is bounded, yet the integral (8) fails to be finite.

When the rank condition fails we use (3) instead.

It is therefore natural to allow (5) to fail when x is not a continuity point of F.

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