** Next:** Distributions and weak limits:
** Up:** ``Strange'' limits
** Previous:** ``Strange'' limits

Consider a sequence:

When
, the sequence converges to the so-called -function (which, by the way, is not a
function but a new object: The * distribution*).
-function equals zero if , is infinitely large if ,
and, additionally, keeps the area under its graph equal to one. This last
extra requirement differs -function from ``normal'' functions. It comes
from the constancy of the integrals

Problem: Prove the basic propety of the -function

for all smooth functions .

*Andre Cherkaev*

*2001-11-16*