Linear Operators: General theory |
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Page 132
... singular , then 2 is also u - singular . 14 THEOREM . ( Lebesgue decomposition ) Let ( S , E , μ ) be a measure space . Then every finite countably additive measure 2 defined on E is uniquely representable as a sum λ = a + ẞ where a is ...
... singular , then 2 is also u - singular . 14 THEOREM . ( Lebesgue decomposition ) Let ( S , E , μ ) be a measure space . Then every finite countably additive measure 2 defined on E is uniquely representable as a sum λ = a + ẞ where a is ...
Page 216
... singular . We may write 2 as the sum of a μ - singular positive measure 2 , and a μ - continuous measure 2. From the definition of the derivative it is clear that dλ / dμ dλ1 / dμ + dλ2 / dμ , μ - almost everywhere . By the part of ...
... singular . We may write 2 as the sum of a μ - singular positive measure 2 , and a μ - continuous measure 2. From the definition of the derivative it is clear that dλ / dμ dλ1 / dμ + dλ2 / dμ , μ - almost everywhere . By the part of ...
Page 564
... singular initial matrix Yo Show that if ft 4 ( s ) ds and A ( t ) commute for each t e I , then the matrix solution ... singular and tr A ( t ) is the sum of the entries on the principal diagonal . Show that a solution matrix Y ( t ) is ...
... singular initial matrix Yo Show that if ft 4 ( s ) ds and A ( t ) commute for each t e I , then the matrix solution ... singular and tr A ( t ) is the sum of the entries on the principal diagonal . Show that a solution matrix Y ( t ) is ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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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 disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ