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Continuous functions are dense in L1(T)

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Mark Pedigo, SLU

What
  • Analysis Seminar
When Tue, Nov 07, 2006
from 02:10 PM to 03:00 PM
Where RH 316
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Abstract: A measurable function f is said to be in L1(R) if ∫ |f| < ∞. These functions play an important role in analysis. We show that any function in L1(R) can be approximated by a continuous function in the L1 norm. More precisely, for any L1(R) function f, given ? > 0 there exists a continuous function g in L1(R) such that the L1 norm of (f-g) is less than ?. We present a proof of this fact, along with a running example to illustrate the concepts of the proof. The talk concludes with an application which sets the stage for the November 14th seminar.

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