## Linear Operators: General theory |

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Page 95

In some cases that will be encountered the values of fi are not scalars, but

customarily where integration is used in this text [x is a scalar valued

/ a vector (or scalar) valued

In some cases that will be encountered the values of fi are not scalars, but

customarily where integration is used in this text [x is a scalar valued

**function**and/ a vector (or scalar) valued

**function**. Thus, even if the integration process is**defined**...Page 101

stS stS If for some null set N the restriction of / to S—N has its values in a

separable set, the

Expressions such as essentially compact valued are

example above, ...

stS stS If for some null set N the restriction of / to S—N has its values in a

separable set, the

**function**/ is said to be //.-essentially separably valued.Expressions such as essentially compact valued are

**defined**similarly. In theexample above, ...

Page 223

5 Let Abea function of bounded variation on the interval (a, b) and continuous on

the right. Let g be a

integral / = jlg(s)dh(s) exists. Let / be a continuous increasing function on an open

...

5 Let Abea function of bounded variation on the interval (a, b) and continuous on

the right. Let g be a

**function defined**on (a, b) such that the Lebesgue-Stieltjesintegral / = jlg(s)dh(s) exists. Let / be a continuous increasing function on an open

...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

44 other sections not shown

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Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero