We provide a variety of results for (quasi)convex, law-invariant functionals defined on a general Orlicz space, which extend well-known results in the setting of bounded random variables. First, we show that Delbaen's dual characterization of the Fatou property, which no longer holds in a general Orlicz space, continues to hold under the assumption of law-invariance. Second, we identify the range of Orlicz spaces where the characterization of the Fatou property in terms of norm lower semicontinuity by Jouini, Schachermayer and Touzi still holds. Third, we extend Kusuoka's dual representation to a general Orlicz space. Finally, we prove a version of the extension result by Filipovi\'{c} and Svindland by replacing norm lower semicontinuity with the (generally non-equivalent) Fatou property. Our results have natural applications to the theory of risk measures.
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