Linear Operators: General theory |
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Page 136
... extension of μ to the o - field E determined by E. Suppose that μ1 is another such extension . If μ is o - finite on Σ to prove the uniqueness of the extension , it will suffice to show that μ ( E ) = μ1 ( E ) for every set E in 2 ...
... extension of μ to the o - field E determined by E. Suppose that μ1 is another such extension . If μ is o - finite on Σ to prove the uniqueness of the extension , it will suffice to show that μ ( E ) = μ1 ( E ) for every set E in 2 ...
Page 143
... extension of μ . The o - field Σ * is known as the Lebesgue extension ( relative to μ ) of the o - field Σ , and the measure space ( S , Σ * , μ ) is the Lebesgue extension of the measure space ( S , E , μ ) . μ Expressions such as u ...
... extension of μ . The o - field Σ * is known as the Lebesgue extension ( relative to μ ) of the o - field Σ , and the measure space ( S , Σ * , μ ) is the Lebesgue extension of the measure space ( S , E , μ ) . μ Expressions such as u ...
Page 554
... Extension of Linear Transformation . Taylor [ 1 ] studied conditions under which the extension of linear functionals will be a uniquely defined operation . Kakutani [ 6 ] showed that this operation is linear and isometric for each ...
... Extension of Linear Transformation . Taylor [ 1 ] studied conditions under which the extension of linear functionals will be a uniquely defined operation . Kakutani [ 6 ] showed that this operation is linear and isometric for each ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ