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Page 39
... contained in no other ideal of the same type . If R contains a unit element e , than any right ideal I。 is contained in a maximal right ideal . To see this , let & be the collection of all right ideals in R which contain I。 and which ...
... contained in no other ideal of the same type . If R contains a unit element e , than any right ideal I。 is contained in a maximal right ideal . To see this , let & be the collection of all right ideals in R which contain I。 and which ...
Page 137
... contained in E and a set G in Σ whose interior contains E such that [ μ ( C ) | < ɛ for every C in with CCG - F ... contained in E , E is contained in the interior of G , and v ( μ , G — F ) < ɛ . Then since v ( μ , G - F ) = μ + ( G – F ) ...
... contained in E and a set G in Σ whose interior contains E such that [ μ ( C ) | < ɛ for every C in with CCG - F ... contained in E , E is contained in the interior of G , and v ( μ , G — F ) < ɛ . Then since v ( μ , G - F ) = μ + ( G – F ) ...
Page 417
... contained in a proper subinterval [ -a , ∞ ) , or ( —∞ , a ] , of the real axis , where a > 0. Let M = NO ( -N ) ; then M = M , and M is a neighborhood of the origin such that f ( M ) is contained in the interval [ —a , a ] . In this ...
... contained in a proper subinterval [ -a , ∞ ) , or ( —∞ , a ] , of the real axis , where a > 0. Let M = NO ( -N ) ; then M = M , and M is a neighborhood of the origin such that f ( M ) is contained in the interval [ —a , a ] . In this ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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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