normal order

Let f(n) and F(n) be functions from +. We say that f(n) has normal order F(n) if for each ϵ>0 the set


has the property that d¯(A(ϵ))=1. Equivalently, if B(ϵ)=+\A(ϵ), then d¯(B(ϵ))=0. (Note that d¯(X) denotes the lower asymptotic density of X).

We say that f has average order F if

Title normal order
Canonical name NormalOrder
Date of creation 2013-03-22 12:36:23
Last modified on 2013-03-22 12:36:23
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 5
Author mathcam (2727)
Entry type Definition
Classification msc 11B05
Defines average order