## Linear Operators: General theory |

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Page 140

An

the forms : [ a , b ] { sla SS sb } , [ a , b ) = { sas < b } , ( a , b ] = { s | a ... The

number a is called the left end point and b the right end point of any of these

An

**interval**is a set of points in the extended real number system which has one ofthe forms : [ a , b ] { sla SS sb } , [ a , b ) = { sas < b } , ( a , b ] = { s | a ... The

number a is called the left end point and b the right end point of any of these

**intervals**.Page 141

Since v ( f , ( c , c + ez ] ) > 8 there are points aj , bin song j n , , ( ) ( ) 0 S ... ng 2 \ /

bi ) - | ( az ) | > d . i = n , + 1 The argument may be repeated by defining Ez = an , -

c and choosing appropriate points in the

Since v ( f , ( c , c + ez ] ) > 8 there are points aj , bin song j n , , ( ) ( ) 0 S ... ng 2 \ /

bi ) - | ( az ) | > d . i = n , + 1 The argument may be repeated by defining Ez = an , -

c and choosing appropriate points in the

**interval**( c , c + £ 3 ] . By induction , it is ...Page 223

5 Let h be a function of bounded variation on the

on the right . Let g be a function defined on ( a , b ) such that the Lebesgue -

Stieltjes integral I Sög ( s ) dh ( s ) exists . Let f be a continuous increasing

function on ...

5 Let h be a function of bounded variation on the

**interval**( a , b ) and continuouson the right . Let g be a function defined on ( a , b ) such that the Lebesgue -

Stieltjes integral I Sög ( s ) dh ( s ) exists . Let f be a continuous increasing

function on ...

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### Contents

Preliminary Concepts 1 1 Preliminary Concepts | 1 |

B Topological Preliminaries 10 B Topological Preliminaries | 10 |

Metric Spaces | 18 |

Copyright | |

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