Differentiation of Integrals in Rn |
Contents
SOME COVERING THEOREMS | 1 |
Covering theorems of the Whitney type | 9 |
Covering theorems of the Vitali type | 19 |
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affine transformation Assume B F basis basis invariant Besicovitch bounded measurable set bounded set choose concludes the proof consider constant convex convex sets covering property covering theorem cubes define density basis density property differentiates ff differentiates L(1 differentiation basis differentiation properties disjoint sequence Euclidean balls finite fixed functions f Guzmán halo conjecture halo function halo problem Hardy-Littlewood maximal operator Hence homothetic integrals intervals centered invariant by homothecies Kakeya Lą(R Lebesgue Lebesgue measure lemma Let us call lím line r(x M₂ Math maximal operator associated Mf(x Nikodym null set obtain open bounded open intervals open set P₁ parallelogram points R₁ and R₂ rectangles REMARKS satisfies side T₁ T₂ Theorem 1.1 theorem of Besicovitch triangles Vitali cover weak type weak type 1,1 x e R˛ Zygmund