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Integrate and measure problem.
Assume $\mu(X)=1$, $f \in L^{p} (X,M,\mu)$ for some $0 I want to prove that: $$\lim_{p\to 0}||f||_p = e^{\int_X \log|f|d \mu}$$ I'm going to prove $\ge$ part using Jensen inequality, but I cannot go opposite side. How can I make it?