Linear Operators: General theory |
From inside the book
Results 1-3 of 82
Page 143
... measure on as well as for its extension on * should cause no confusion . The measure of Lebesgue in an interval [ a , b ] of real numbers may be defined as the Lebesgue extension of the Borel measure in [ a , b ] . The Lebesgue measurable ...
... measure on as well as for its extension on * should cause no confusion . The measure of Lebesgue in an interval [ a , b ] of real numbers may be defined as the Lebesgue extension of the Borel measure in [ a , b ] . The Lebesgue measurable ...
Page 188
... measure has the property n = 1 n n μ ( Ï E1 ) = ÏÏ μ ‚ ( E ̧ ) , Π μ . ( Ε . ) , i = 1 i = 1 Ε , Ε Σ and it follows ... Lebesgue measure on the real line for i = 1 , ... , n . Then S = P1 S ; is n - dimensional Eucli- dean space , and u ...
... measure has the property n = 1 n n μ ( Ï E1 ) = ÏÏ μ ‚ ( E ̧ ) , Π μ . ( Ε . ) , i = 1 i = 1 Ε , Ε Σ and it follows ... Lebesgue measure on the real line for i = 1 , ... , n . Then S = P1 S ; is n - dimensional Eucli- dean space , and u ...
Page 223
... Lebesgue measure and that f ' may vanish almost everywhere without f being a constant . 7 Let ( S , E , μ ) be the product of the regular measure spaces ( Sa , Ex , μg ) , α e A. If S is endowed with its product topology show that ( S ...
... Lebesgue measure and that f ' may vanish almost everywhere without f being a constant . 7 Let ( S , E , μ ) be the product of the regular measure spaces ( Sa , Ex , μg ) , α e A. If S is endowed with its product topology show that ( S ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
59 other sections not shown
Other editions - View all
Common terms and phrases
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