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A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls

A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls

Negative association for a family of random variables $(X_i)$ means that for any coordinatewise increasing functions $f,g$ we have $$\mathbb{E} f(X_{i_1},\ldots,X_{i_k}) g(X_{j_1},\ldots,X_{j_l}) \leq \mathbb{E} f(X_{i_1},\ldots,X_{i_k}) \mathbb{E} g(X_{j