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The variation of a class of Orlicz moments with respect to the Asplund sumwithin the class of log-concave functions is demonstrated. Such a variationalformula naturally leads to a family of dual Orlicz curvature measures forlog-concave functions. They are functional analogs of dual (Orlicz) curvaturemeasures for convex bodies. Partial existence results for the functional dualOrlicz Minkowski problem are shown.

The dual Orlicz curvature measures for log-concave functions and their related Minkowski problems