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I am studying Bernsteins theorem on completely monotone functions and in the proof I need the uniform convergence of the sequence of functions: for $t>0$ define $h_n(t):=(1-\frac{\lambda t}{n})_{+}^{n-1}$ (where $a_{+}=\max(0,a)$) against the exponentialfunction, i.e. $(t\mapsto e^{-\lambda t})$.

I have tried elementary proofs but cant find a way to proof it. I would be very thankful for help!

broki
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    You need to do some work and you need to specify the domain. – copper.hat Jun 01 '23 at 17:34
  • thank you for your answer. I did not add my domain, which is a big mistake because I nedd the uniform convergence on the positive real numbers, i.e. $t>0$ in this context., $\lambda >0$ is a fixed constant. – broki Jun 02 '23 at 10:09

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