## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 91

Page 95

Finitely Additive Set

process is defined with respect to a scalar

integral v may ...

Finitely Additive Set

**Functions**In contrast to the terms real**function**, complex**function**, etc., where the adjectives real and ... Thus, even if the integrationprocess is defined with respect to a scalar

**valued**set**function**u, the resultingintegral v may ...

Page 119

(b) the

measurable. Next suppose that we consider a

say ...

(b) the

**function**g defined by g(s) = f(s) if s 6 St. US-, g(s) = 0 if s e S+ US-, is u-measurable. Next suppose that we consider a

**function**f (vector or extended real-**valued**) which is defined only on the complement of a u-null set NC S. Then wesay ...

Page 196

...

between Lebesgue spaces (cf. Section VI.8) one is faced with the following

situation. Suppose that (S, 2, u) is a measure space and F is a p-measurable

...

**valued**integrals to concrete problems such as the representation of operatorsbetween Lebesgue spaces (cf. Section VI.8) one is faced with the following

situation. Suppose that (S, 2, u) is a measure space and F is a p-measurable

**function**...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

### Other editions - View all

### Common terms and phrases

additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero