Proving Equality Using Lebesgue Monotone Convergence Theorem

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SUMMARY

The discussion centers on using the Lebesgue Monotone Convergence Theorem to prove a specific equality involving an integral. The integral in question is confirmed to be \int_0^1 \frac{x^p}{x-1} \log (x) dx, with the measure dm(x) = dx. One participant successfully identified a suitable monotonic sequence derived from power series to complete the proof.

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  • Understanding of the Lebesgue Monotone Convergence Theorem
  • Familiarity with integrals and their properties
  • Knowledge of power series and their convergence
  • Basic concepts of measure theory
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  • Explore the properties of integrals involving logarithmic functions
  • Learn about constructing monotonic sequences from power series
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Homework Statement


use the Lebesgue monotone convergence theorem to prove the following equality (attached)


Homework Equations


Lebesgue monotone convergence theorem


The Attempt at a Solution


i tried to identify a suitable monotonic sequence,from power series.
 

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hedipaldi said:

Homework Statement


use the Lebesgue monotone convergence theorem to prove the following equality (attached)


Homework Equations


Lebesgue monotone convergence theorem


The Attempt at a Solution


i tried to identify a suitable monotonic sequence,from power series.

The integral is not clear (poor quality image). Is it
[tex]\int_0^1 \frac{x^p}{x-1} \log (x) dx?[/tex] Do you mean dm(x) = dx?

RGV
 
yes,this is correct.
I already solved .Thank's a lot.
 

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