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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 ...
... 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 ...
Page 186
... measure with the desired properties . prove the uniqueness of μ , we note that it follows in the same way that the ... measure space ( S , E , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn ...
... measure with the desired properties . prove the uniqueness of μ , we note that it follows in the same way that the ... measure space ( S , E , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn ...
Page 405
... measure zero ; the measure μ is not countably additive . In fact , using the relation between μ∞ and м , it is easy to see that l is the union of a countable family of u - null sets . These relationships may be summed up in the ...
... measure zero ; the measure μ is not countably additive . In fact , using the relation between μ∞ and м , it is easy to see that l is the union of a countable family of u - null sets . These relationships may be summed up in the ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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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