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Hessian measures II
In our previous paper on this topic, we introduced the notion of k-Hessian
measure associated with a continuous k-convex function in a domain \Om in
Euclidean n-space, k=1,...,n, and proved a weak continuity result with respect
to local uniform convergence. In this paper, we consider k-convex functions,
not necessarily continuous, and prove the weak continuity of the associated
k-Hessian measure with respect to convergence in measure. The proof depends
upon local integral estimates for the gradients of k-convex functions.Comment: 26 pages, published versio
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