## Linear Operators, Part 1 |

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Page 39

A right ( left , or two - sided ) ideal in a ring R is called a maximal right ( left , or

two - sided ) ideal , if it is

the collection of all right ideals in R which

A right ( left , or two - sided ) ideal in a ring R is called a maximal right ( left , or

two - sided ) ideal , if it is

**contained**in no other ideal of the ... To see this , let & bethe collection of all right ideals in R which

**contain**1 , and which do not**contain**e .Page 137

An additive set function и M defined on a field of subsets of a topological space S

is said to be regular if for each Ee and ε > 0 there is a set F in whose closure is

An additive set function и M defined on a field of subsets of a topological space S

is said to be regular if for each Ee and ε > 0 there is a set F in whose closure is

**contained**in E and a set G in whose interior contains E such that su ( C ) | < ε for ...Page 417

In this case , f ( ea - 1M ) is

neighborhood of the origin , f is continuous at 0. By Lemma II.1.3 , s is continuous

. Q.E.D. Lemma 7 and Theorem 1.12 yield the following result . 8 THEOREM .

In this case , f ( ea - 1M ) is

**contained**in the interval [ - € , ɛ ] . Since ea - M is aneighborhood of the origin , f is continuous at 0. By Lemma II.1.3 , s is continuous

. Q.E.D. Lemma 7 and Theorem 1.12 yield the following result . 8 THEOREM .

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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