## Linear Operators: General theory |

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Page 177

H III.10.3 RADON - NIKODÝM THEOREM 177 n EC En - n E E n - 00 n - O may be

H III.10.3 RADON - NIKODÝM THEOREM 177 n EC En - n E E n - 00 n - O may be

**assumed**that 2 is real valued . ... represented as the difference of its positive and negative variations ( 4.11 ) and so we may also**assume**that 2 is positive .Page 278

If the algebras C ( S ) and C ( T ) are over the field of complex numbers , it is also

If the algebras C ( S ) and C ( T ) are over the field of complex numbers , it is also

**assumed**that II1 = IIf . Then II is continuous and has the form ( H } ) ( t ) = f ( h ( t ) ) , tet , 1 € C ( S ) , where h is a continuous map ...Page 326

E € Evidently we may

E € Evidently we may

**assume**that Ox 52 - k . Let nx > 0 be such that if A € and 2 ( A ) < nx ... Since fre was**assumed**to converge u - almost everywhere to f , we conclude that the sequence { 8x } converges u - almost everywhere to f .### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc Proof properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero