Linear Operators: General theory |
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Page 143
... 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 sets in [ a , b ] are the sets in the Lebesgue extension ( relative to Borel measure ) ...
... 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 sets in [ a , b ] are the sets in the Lebesgue extension ( relative to Borel measure ) ...
Page 218
... Lebesgue set of f contains each point of continuity of f . Let us suppose that f is a vector valued Lebesgue integrable function of one real variable t , ∞ < t < ∞ . Let n Qn ( t ) t≤ == 0 , t > 2 Theorem 9 states , in somewhat ...
... Lebesgue set of f contains each point of continuity of f . Let us suppose that f is a vector valued Lebesgue integrable function of one real variable t , ∞ < t < ∞ . Let n Qn ( t ) t≤ == 0 , t > 2 Theorem 9 states , in somewhat ...
Page 223
... Lebesgue - Stieltjes integral I = Såg ( s ) dh ( s ) exists . Let ƒ be a continuous increasing function on an open interval ( c , d ) , with f ( c ) = a , f ( d ) = b . Show that the Lebesgue - Stieltjes integral exists and is equal to ...
... Lebesgue - Stieltjes integral I = Såg ( s ) dh ( s ) exists . Let ƒ be a continuous increasing function on an open interval ( c , d ) , with f ( c ) = a , f ( d ) = b . Show that the Lebesgue - Stieltjes integral exists and is equal to ...
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