Under the basic assumptions of classic g-expectations,the convexity,conditional convexity and Ft-convexity for g-expectations in Lpspace(1＜p≤+∞)are studied,and is established the relationship between the generators of backward stochastic differential equations(BSDEs for short)and these properties of g-expectations.Furthermore,the correspondence between the theory of g-expectations and the dynamic(resp.static)convex risk measures induced by g-expectations are obtained.
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