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Results tagged with lebesgue-integral
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user 751096
For questions about integration, where the theory is based on measures. It is almost always used together with the tag [measure-theory], and its aim is to specify questions about integrals, not only properties of the measure.
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If $f$ is Lebesgue integrable, then show that $h(u)=\int_{\mathbb{R}} e^{iux} f(x) dx$ , for...
Suppose we have a function $h$ which is continuous and Lebesgue integrable on $\mathbb{R}$.
We have $f(x)=\frac{1}{2 \pi} \int_{\mathbb{R}} e^{-iux} h(u) du $, for all real $x$.
If $f$ is Lebesgue …
- 721
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Example of a function on a probability space
I was asked by one of teachers to find a probability space $(\Omega,\mathcal{F},\mu)$ and a real valued integrable function $f$ on this space which is unbounded.
I gave it a try but I think I am miss …
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