Uniqueness of the best monotone approximation in L^Φ([a,b]) for approximately continuous f is obtained by proving continuity of the best approximation set for suitable convex Φ.
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On the Uniqueness of Best Non-decreasing Approximation in Orlicz Spaces
Uniqueness of the best monotone approximation in L^Φ([a,b]) for approximately continuous f is obtained by proving continuity of the best approximation set for suitable convex Φ.