On 9 อมา, 17:53, "Joubert" <luckyguy675...@hotmail.com> wrote:
> Exhibite a function which is in L1 but such that lim x-> +inf f(x) is not > zero.
Do you mean L1(R)? If f is i L1(R) then ||f,L1(R)|| = integral{| f(x)|} < 0 => f(x) - > 0 when |x|->inf . If f(x) is not 0 when x -> inf then integral{|f(x)|} doesn't exist!
The World Wide Wade <aderamey.a...@comcast.net> writes:
> In article <47d3cfb2$0$4794$4fafb...@reader4.news.tin.it>, > "Joubert" <luckyguy675...@hotmail.com> wrote:
> > Exhibite a function which is in L1 but such that lim x-> +inf f(x) is > > not > > zero.
> How about the characteristic function of the integers?
Of course this is equal almost everywhere to (and thus is the same member of L1 as) a function for which the limit is 0. You might want to modify the example by taking small intervals around the integers. -- Robert Israel isr...@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada
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