## Linear Operators: General theory |

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Let a , u be finitely additive set functions defined on a field E. Then a is said to be continuous with respect to u or simply u - continuous , if lim 2 ( E ) = 0 . v ( 1 , E ) - 0 The function à is said to be u -

Let a , u be finitely additive set functions defined on a field E. Then a is said to be continuous with respect to u or simply u - continuous , if lim 2 ( E ) = 0 . v ( 1 , E ) - 0 The function à is said to be u -

**singular**if there is a ...Page 132

It follows easily from Definition 12 that if 2 , non , n = - 1 , 2 , ... , are finite countably additive measures with an ( E ) — 2 ( E ) , EE , and if an , n = 1 , 2 , ... are u -

It follows easily from Definition 12 that if 2 , non , n = - 1 , 2 , ... , are finite countably additive measures with an ( E ) — 2 ( E ) , EE , and if an , n = 1 , 2 , ... are u -

**singular**, then a is also u -**singular**. 14 THEOREM .Page 743

On the existence of certain

On the existence of certain

**singular**integrals . Acta Math . 88 , 85–139 ( 1952 ) . 5. On**singular**integrals . Amer . J. Math . 78 , 289-309 ( 1956 ) . 6. Algebras of certain**singular**operators . Amer . J. Math . 78 , 310–320 ( 1956 ) .### 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