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Page 729
... Ergodic theorems of the mean type , but in which other methods of summation replace the ( C , 1 ) -method ordinarily used , are proved by Cohen [ 2 ] , Hille [ 1 ; Chap . 14 ] and Phillips [ 4 ] . Pointwise ergodic theorem . This theorem ...
... Ergodic theorems of the mean type , but in which other methods of summation replace the ( C , 1 ) -method ordinarily used , are proved by Cohen [ 2 ] , Hille [ 1 ; Chap . 14 ] and Phillips [ 4 ] . Pointwise ergodic theorem . This theorem ...
Page 749
... theorem of Lebesgue . Mat . Sbornik N. S. 20 ( 62 ) , 317-329 ( 1947 ) ... theorem . Pacific J. Math . 1 , 353–367 ( 1951 ) . Dunford , N. ( see also Bartle , R. G. ... ergodic theorem for non - commutative transformations . Acta Sci . Math ...
... theorem of Lebesgue . Mat . Sbornik N. S. 20 ( 62 ) , 317-329 ( 1947 ) ... theorem . Pacific J. Math . 1 , 353–367 ( 1951 ) . Dunford , N. ( see also Bartle , R. G. ... ergodic theorem for non - commutative transformations . Acta Sci . Math ...
Page 770
... theorem in the calculus of probability . Trans . Amer . Math . Soc . 59 , 401-414 ( 1946 ) . 3. On some connections ... ergodic theorem . Ann . of Math . ( 2 ) 42 , 523-537 ( 1941 ) . Concrete representation of abstract ( M ) -spaces ...
... theorem in the calculus of probability . Trans . Amer . Math . Soc . 59 , 401-414 ( 1946 ) . 3. On some connections ... ergodic theorem . Ann . of Math . ( 2 ) 42 , 523-537 ( 1941 ) . Concrete representation of abstract ( M ) -spaces ...
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 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ