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Page 143
... measure on Σ 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 Σ 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 μ ( P E ̧ ) = ÏÏ μ ‚ ( E . ) , i = 1 i = 1 Ε ε Σύ , and it follows from the ... Lebesgue measure on the real line for i n . Then S = P1 S ; is n - dimensional Eucli- Xμn is known as n - dimensional Borel ...
... measure has the property n = 1 n μ ( P E ̧ ) = ÏÏ μ ‚ ( E . ) , i = 1 i = 1 Ε ε Σύ , and it follows from the ... Lebesgue measure on the real line for i n . Then S = P1 S ; is n - dimensional Eucli- Xμn is known as n - dimensional Borel ...
Page 223
... Lebesgue measure and that f ' may vanish almost everywhere without ƒ being a constant . Let ( S , E , μ ) be the product of the regular measure spaces ( Sα , Eα , Ma ) , α € A. If S is endowed with its product topology show that ( S , E ...
... Lebesgue measure and that f ' may vanish almost everywhere without ƒ being a constant . Let ( S , E , μ ) be the product of the regular measure spaces ( Sα , Eα , Ma ) , α € A. If S is endowed with its product topology show that ( S , E ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ