## Linear Operators: General theory |

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Page 140

It can also be extended by defining the measure differently on the basic field E.

We shall illustrate this latter remark by describing here the construction of a

Radon measure on an

It can also be extended by defining the measure differently on the basic field E.

We shall illustrate this latter remark by describing here the construction of a

Radon measure on an

**interval**. 15 Definition. An**interval**is a set of points in the ...Page 141

a„i+1 ^ 6„i+1 ^ c+enj = aBi and such that <-n,+l The argument may be repeated

by defining es = a^—c and choosing appropriate points in the

By induction, it is clear that for every integer k = 1, 2, . . ., there are points a,, 6<

with ...

a„i+1 ^ 6„i+1 ^ c+enj = aBi and such that <-n,+l The argument may be repeated

by defining es = a^—c and choosing appropriate points in the

**interval**(c, c+e8].By induction, it is clear that for every integer k = 1, 2, . . ., there are points a,, 6<

with ...

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 / = J*g(«)dA(s) exists. Let / be a continuous increasing function on an ...

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 / = J*g(«)dA(s) exists. Let / be a continuous increasing function on an ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

78 other sections not shown

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