Math 7770: Analysis and Probability on Infinite-Dimensional Spaces
نویسنده
چکیده
• Rn has a natural measure space structure; namely, Lebesgue measure m on the Borel σalgebra. The most important property of Lebesgue measure is that it is invariant under translation. This leads to nice interactions between differentiation and integration, such as integration by parts, and it gives nice functional-analytic properties to differentiation operators: for instance, the Laplacian ∆ is a self-adjoint operator on the Hilbert space L2(Rn,m).
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تاریخ انتشار 2012