Question: Show that the function (mathbb{R} i x mapsto exp left(-x^{alpha}ight)) is (lambda^{1}(d x))-integrable over the set ([0, infty)) for every (alpha>0). [find integrable majorants (u)

Show that the function \(\mathbb{R} i x \mapsto \exp \left(-x^{\alpha}ight)\) is \(\lambda^{1}(d x)\)-integrable over the set \([0, \infty)\) for every \(\alpha>0\).

[find integrable majorants \(u\) resp. \(w\) if \(0 \leqslant x \leqslant 1\) resp. \(1

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