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Based on both the fundamental theorem of affine geometry in regular$L^0$-modules and the recent progress in random convex analysis, this papercharacterizes the stable fully order preserving and order reversing operatorsacting on the class of proper lower semicontinuous $L^0$-convex functions incomplete random normed modules.

Order preserving and order reversing operators on the class of $L^0$-convex functions in complete random normed modules