Linear Operators: General theory |
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Page 136
... extension of μ to the o - field Zo determined by E. Suppose that is another such extension . If u is σ - 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 Zo determined by E. Suppose that is another such extension . If u is σ - 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 , Σ , 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 , Σ , 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
Preliminary Concepts | 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ