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Consider a sequence:
, 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 .