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Page 226
... integral theo- rem states that √g f ( x ) dx = 0 . The validity of this ... integral theorem may be reworded in a somewhat more gener- al form . To state this ... square mesh , and let U be the union of all open squares of the mesh whose ...
... integral theo- rem states that √g f ( x ) dx = 0 . The validity of this ... integral theorem may be reworded in a somewhat more gener- al form . To state this ... square mesh , and let U be the union of all open squares of the mesh whose ...
Page 469
... integral x ) dx1 · I ( t ) = | ... | Do ( t ; 2 ) da ... S dxn . It is clear ... integral sign and employ [ * ] to conclude that I ' ( t ) is a sum of ... square root { 1- ( x2 + ... .. + x + x + 1 + ... + a2 ) } 1/2 , and a denote ...
... integral x ) dx1 · I ( t ) = | ... | Do ( t ; 2 ) da ... S dxn . It is clear ... integral sign and employ [ * ] to conclude that I ' ( t ) is a sum of ... square root { 1- ( x2 + ... .. + x + x + 1 + ... + a2 ) } 1/2 , and a denote ...
Page 781
... integrable square of the system of differential equations . -y ' + P ( t ) y = hy . Doklady Akad . Nauk SSSR ( N. S. ) 95 , 217-220 ( 1954 ) . ( Russian ) Math . Rev. 15 , 957 ( 1954 ) . Lifšic , I. M. 1 . 2 . On the theory of regular ...
... integrable square of the system of differential equations . -y ' + P ( t ) y = hy . Doklady Akad . Nauk SSSR ( N. S. ) 95 , 217-220 ( 1954 ) . ( Russian ) Math . Rev. 15 , 957 ( 1954 ) . Lifšic , I. M. 1 . 2 . On the theory of regular ...
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