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Page 131
... singular if there is a set Ee such that v ( u , Eo ) = 0 ; 2 ( E ) = 2 ( EE ) , ΕΕΣ . It is clear that the only set function which is both u - singular and μ - continuous is the set function identically zero . If λ , u are both scalar ...
... singular if there is a set Ee such that v ( u , Eo ) = 0 ; 2 ( E ) = 2 ( EE ) , ΕΕΣ . It is clear that the only set function which is both u - singular and μ - continuous is the set function identically zero . If λ , u are both scalar ...
Page 132
... singular , then 2 is also u - singular . Ε 14 THEOREM . ( Lebesgue decomposition ) Let ( S , E , u ) be a measure space . Then every finite countably additive measure λ defined on Z is uniquely representable as a sum λ = a + ẞ where a ...
... singular , then 2 is also u - singular . Ε 14 THEOREM . ( Lebesgue decomposition ) Let ( S , E , u ) be a measure space . Then every finite countably additive measure λ defined on Z is uniquely representable as a sum λ = a + ẞ where a ...
Page 743
... singular integrals . Acta Math . 88 , 85–139 ( 1952 ) . On singular integrals . Amer . J. Math . 78 , 289–309 ( 1956 ) . 6. Algebras of certain singular operators . Amer . J. Math . 78 , 310–320 ( 1956 ) . Calkin , J. W. 1 . 2 ...
... singular integrals . Acta Math . 88 , 85–139 ( 1952 ) . On singular integrals . Amer . J. Math . 78 , 289–309 ( 1956 ) . 6. Algebras of certain singular operators . Amer . J. Math . 78 , 310–320 ( 1956 ) . Calkin , J. W. 1 . 2 ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ