By Abraham Ginzburg
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Extra info for Algebraic Theory of Automata
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In the sequel we denote by 0a generic open set in Rd. If J-L is a nonnegative Borel measure in 0we say that J-L is concentrated on a Borel set F if J-L(O \ F) = O. For a Borel set F c 0, the restriction J-L L F is defined by J-L L F(E) := J-L(F n E) for any Borel set E c O. THE CHAIN RULE FOR THE DIVERGENCE OF VECTOR FIELDS 35 11 The same operation can be defined for vector valued measures with finite total variation in O . Unless otherwise stated, weak* convergence of measures is under stood in the duality with continuous and compactly supported functions.
Algebraic Theory of Automata by Abraham Ginzburg