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We give a truly elementary proof of the convexity of metric adjusted skewinformation following an idea of Effros. We extend earlier results of weakforms of superadditivity to general metric adjusted skew informations.Recently, Luo and Zhang introduced the notion of semi-quantum states on abipartite system and proved superadditivity of the Wigner-Yanase-Dyson skewinformations for such states. We extend this result to general metric adjustedskew informations. We finally show that a recently introduced extension toparameter values $ 1<p\le 2 $ of the WYD-information is a special case of(unbounded) metric adjusted skew information.

Metric adjusted skew information: Convexity and restricted forms of superadditivity