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In this talk,we introduce a weighted Carleson measure dvE,w associated to the family E,where E ={Er(x)}r∈I,x∈X is a family of open subsets of a topological space X endowed with a nonnegative Borel measure satisfying certain basic conditions.Using Calderón-Zygmund theory,we show that the weighted BMO associated with the family E can be characterized by the weighted Carleson measure dvE,w.