Show that for \(\alpha \in(0,1)\) the function \(Z \mapsto \mathbb{E}\left(|Z|^{\alpha}ight)\) is subadditive and complete the argument in the proof of Theorem 10.1 for this case.

Data From Theorem 10.1

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10.1 Theorem (Kolmogorov 1934; Slutsky 1937; Chentsov 1956). Denote by ((x))xen a stochastic process on (Q,,P) with values in Rd and index set R.". If E((x)-(y))