Hausdorff Measures and Functions of Bounded Quadratic Variation
نویسنده
چکیده
To each function f of bounded quadratic variation we associate a Hausdorff measure μf . We show that the map f → μf is locally Lipschitz and onto the positive cone of M[0, 1]. We use the measures {μf : f ∈ V2} to determine the structure of the subspaces of V 0 2 which either contain c0 or the square stopping time space S2.
منابع مشابه
Measure Theory
These are some brief notes on measure theory, concentrating on Lebesgue measure on Rn. Some missing topics I would have liked to have included had time permitted are: the change of variable formula for the Lebesgue integral on Rn; absolutely continuous functions and functions of bounded variation of a single variable and their connection with Lebesgue-Stieltjes measures on R; Radon measures on ...
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