superadditivity
in [Math]
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From: Victor Bapst on 6 May 2010 15:42 Hello everyone, here is a little problem I have. Let u_n bet a superadditive sequence, that is u_(n+m) >= u_m + u_n for all n,m it is quite easy to show that : lim n-> infty u_n/n = sup_n u_n/n exists. Let denote L this limit. Now I want to show that : L = lim m-> infty lim_inf n-> infty (u_(m+n) - u_n)/m May anyone help me ? Thank you very much ! victor
From: Robert Israel on 6 May 2010 21:07 Victor Bapst <vbapst(a)gmail.com> writes: > Hello everyone, > > here is a little problem I have. > Let u_n bet a superadditive sequence, that is > > u_(n+m) >= u_m + u_n > for all n,m > > it is quite easy to show that : lim n-> infty u_n/n = sup_n u_n/n > exists. Let denote L this limit. Does it exist? What about u_n = n^2? Or do you count infinity as "exists"? -- Robert Israel israel(a)math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada
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