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Page 344
... C ( I ) determines an isometric isomorphism between C ( I ) * and NBV ( I ) . Show that if { g } is a sequence of functions in NBV ( I ) , we have lim , → Sıf ( 8 ) dgn ( 8 ) = √1f ( s ) dg ( s ) for all fin C ( I ) if and only if ( i ) ...
... C ( I ) determines an isometric isomorphism between C ( I ) * and NBV ( I ) . Show that if { g } is a sequence of functions in NBV ( I ) , we have lim , → Sıf ( 8 ) dgn ( 8 ) = √1f ( s ) dg ( s ) for all fin C ( I ) if and only if ( i ) ...
Page 558
... ( c ) I - = ΣΕ ( Λ ) . λεσ ( Τ ) Let { 1 , ... , 2 } be an enumeration of σ ( T ) , and let X It follows from ( b ) and ( c ) of Theorem 6 that xx1 ...ぎょ X. = E ( 2 ; ) X . Moreover , since TE ( 2 ) = E ( 2 ) T , it follows that TX , CX ...
... ( c ) I - = ΣΕ ( Λ ) . λεσ ( Τ ) Let { 1 , ... , 2 } be an enumeration of σ ( T ) , and let X It follows from ( b ) and ( c ) of Theorem 6 that xx1 ...ぎょ X. = E ( 2 ; ) X . Moreover , since TE ( 2 ) = E ( 2 ) T , it follows that TX , CX ...
Page 827
... c ( 239 ) Co ( 239 ) f ( 410 ) ca ( S , Σ ) ( 240 ) ca ( S , Σ , X ) ( 161 ) co ( 4 ) ( 414 ) || ID ( 239 ) ( 239 ) co ( 4 ) ( 414 ) ( 238 ) Cs ( 240 ) In ( 239 ) C " ( I ) ( 242 ) limƒ ( a ) → rg ( a ) ( 26 ) C ( S ) ( 240 ) lim infan ...
... c ( 239 ) Co ( 239 ) f ( 410 ) ca ( S , Σ ) ( 240 ) ca ( S , Σ , X ) ( 161 ) co ( 4 ) ( 414 ) || ID ( 239 ) ( 239 ) co ( 4 ) ( 414 ) ( 238 ) Cs ( 240 ) In ( 239 ) C " ( I ) ( 242 ) limƒ ( a ) → rg ( a ) ( 26 ) C ( S ) ( 240 ) lim infan ...
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