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In this paper, we establish representation theorems for generators ofbackward stochastic differential equations (BSDEs in short) in probabilityspaces with general filtration from the perspective of transposition solutionsof BSDEs. As applications, we give a converse comparison theorem for generatorsof BSDEs and also some characterizations to positive homogeneity, independenceof y, subadditivity and convexity of generators of BSDEs. Then, we extendconcepts of g-expectations and conditional g-expectations to the probabilityspaces with general filtration and investigate their properties.

Representation theorems for generators of BSDEs and the extended g-expectations in probability spaces with general filtration