**Marsden, J. E.
**

It is well known that Lebesgue's dominated convergence theorem does not hold for nets; that is, having a countable sequence is essential. On the other hand, for a real valued function on an interval, sequences do suffice; that is,
*f* (*x*) = *a* iff*f* (*x*_{n}) = *a*
for every sequence *x*_{n}*y*
. The purpose of this note is to isolate the basic reasons for these phenomena.