Per Widipedia: Intuitively, the lemma says that if a function oscillates rapidly around zero, then the integral of this function will be small. The integral will approach zero as the number of oscillations increases.
Yep, for any interval I of the real line, real variable t, and any Lebesgue integrable function f as t approaches infinity, the integral of f(x)e^itx dx = 0.
But that is not my interest. My interest is in the result of nought carry nought, as tought in the Jethero Bodine skool of mathematics.