Chapter 10 exercises

Let $\boldsymbol{X}$ be a random variable and let $1 \leq r \leq \infty$. Recall that the triangle (Minkowski) inequality implies that for real-valued functions $f_1, f_2$, $\|f_1(\boldsymbol{X}) + f_2(\boldsymbol{X})\|_r \leq \|f_1(\boldsymbol{X})\|_r + \|f_2(\boldsymbol{X})\|_r.$ More generally, if $w_1, \dots, w_m$ are nonnegative reals summing to $1$ and $f_1, \dots, f_m$ are real functions [...]

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