Normal Order

$f(n)$ has the normal order $F(n)$ if $f(n)$ is approximately $F(n)$ for Almost All values of $n$. More precisely, if

$$(1-\epsilon)F(n)<f(n)<(1+\epsilon)F(n)$$

for every positive $\epsilon$ and Almost All values of $n$, then the normal order of $f(n)$ is $F(n)$.

See also Almost All

References

Hardy, G. H. and Weight, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Oxford University Press, p. 356, 1979.