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If a real-valued $f(t)$ is absolute continuous on a domain $[a,\,b]$, Does it imply it is also absolute integrable $\int_a^b |f(t)|dt < \infty$?
If a real-valued $f(t)$ is absolute continuous on a domain $[a,\,b]$, Does it imply it is also absolute integrable $\int_a^b |f(t)|dt < \infty$?
If is not true in general, please give some counter-...
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Deducing properties of the $\ell_3$ norm from the $\ell_1$ and $\ell_2$ norms
Suppose we have a function $f: [0,1] \rightarrow \mathbb{R}$, $f(x) \geq 0$ normalised so that $\|f\|_1 = 1$, where
$$
\| f\|_p = \left( \int_0^1 f(x)^p d x \right)^{1/p}.
$$
Moreover, we know that $\|...
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