Difference between revisions of "Convergence of a sequence"

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{{Todo|preserve "interesting" example}}
 
{{Todo|preserve "interesting" example}}

Latest revision as of 13:30, 5 December 2015

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TODO: preserve "interesting" example


Interesting examples

fn(t)=tn0 in L1

Using the L1 norm stated here for convenience: fLp=(10|f(x)|pdx)1p so fL1=10|f(x)|dx

We see that fnL1=10xndx=[1n+1xn+1]10=1n+1

This clearly 0 - this is 0:[0,1]R which of course has norm 0, we think of this from the sequence (fn0L1)n=10fn0