$(\int(\int f(x,y) dy)^p dx)^{\frac{1}{p}} \leq \int(\int f(x,y)^p dx)^{\frac{1}{p}} dy $

Question

If $f: \mathbb{R}^2: \to \mathbb{R}$ measurable Lebesgue positive then for $ 1 ≤ p ≤ ∞$

$(\int(\int f(x,y) dy)^p dx)^{\frac{1}{p}} \leq \int(\int f(x,y)^p dx)^{\frac{1}{p}} dy $ .

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