Question

Prove $ \int_0^t \frac{\lambda a_z}{1+\frac{p}{1-p}e^{-\int_0^z \lambda a_s ds}} dz = \log(p + (1-p)e^{\int_0^t \lambda a_s ds}) $

score 45 · Answer 1 · 2019-11-03 12:46:04

45

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Prove $ \int_0^t \frac{\lambda a_z}{1+\frac{p}{1-p}e^{-\int_0^z \lambda a_s ds}} dz = \log(p + (1-p)e^{\int_0^t \lambda a_s ds}) $

Published on 03 Nov 2019 - 12:46

score 43 · Answer 2 · 2019-11-03 22:44:09

43

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score 92 · Answer 3 · 2019-11-03 23:03:09

92

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score 439 · Answer 6 · 2019-11-04 00:53:09

439

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score 403 · Answer 7 · 2019-11-05 06:23:56

403

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636

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List Question

Prove $ \int_0^t \frac{\lambda a_z}{1+\frac{p}{1-p}e^{-\int_0^z \lambda a_s ds}} dz = \log(p + (1-p)e^{\int_0^t \lambda a_s ds}) $

Integrability of function related to convergence of infinite sum

Understanding what Im supposed to prove in the following Fatou´s generalized lemma.

Proving the Continuity of Integration (Royden)

Example of sequence with no dominating function but is uniformly integrable so limit holds

If $fh\in \mathcal{L}^1(\mu )$ for every $h\in \mathcal{L}^{p'}(\mu )$ then $f\in \mathcal{L}^p(\mu)$

Proving that $\mathbb Q\cap [0,1]$ is a null subset of $\mathbb R$

Local integrability of $g(x_1,x_2,x_3)=\frac{x_1}{{\left\lVert x\right\rVert}^3}$

$f_n \rightarrow f$ pointwise a.e. does not hold for integral

How to get the last step?

Integrable functions that decay slower than every polynomially integrable function

Does graph of a monotone function have measure zero?

Understanding proof when equality holds in Minkowski's inequality

Proof relating to sum of Lebesgue integrable functions

Evaluating a Lebesgue Integral

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