Differentiation of sets in measure |
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| Authors: | Está te V. Khmaladze |
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| Affiliation: | Victoria University of Wellington, School of Mathematics, Statistics and Computer Science, PO Box 600, Wellington, New Zealand |
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| Abstract: | ![]()
Suppose F(ε), for each ε∈[0,1], is a bounded Borel subset of Rd and F(ε)→F(0) as ε→0. Let A(ε)=F(ε)?F(0) be symmetric difference and P be an absolutely continuous measure on Rd. We introduce the notion of derivative of F(ε) with respect to ε, dF(ε)/dε=dA(ε)/dε, such that |
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| Keywords: | Local Steiner formula Local point process Set-valued mapping |
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