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Answer by saz for Application of Fatou's lemma to show that a function is the...
Define $A_k := \{ x \in X \mid f(x) \geq 1+1/k\}$, then by assumption$$C = \int_X f(x)^n \, \mu(dx) \geq \int_{A_k} f(x)^n \, \mu(dx) \geq \left(1+ \frac{1}{k} \right)^n \mu(A_k)$$for any $n \in...
View ArticleApplication of Fatou's lemma to show that a function is the characteristic of...
I need some help solving this problem:Let $(X,\mathcal{M},\mu)$ be a measure space and $f:X\mapsto[0,\infty]$ be a $\mu-$measurable function such that there exists $C\geq0$ such that...
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