## Linear Operators: General theory |

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Page 202

We will first show that /n is

with the stated value on elementary sets. For each n let /nn, Xn be set functions

on En defined by the formulas = MKxS«>). UK) = E„eZn. Then xtrt aen acn and so

, ...

We will first show that /n is

**unique**. Let A be another additive set function on Exwith the stated value on elementary sets. For each n let /nn, Xn be set functions

on En defined by the formulas = MKxS«>). UK) = E„eZn. Then xtrt aen acn and so

, ...

Page 276

... Theorem 18, that the functions of 21 distinguish between the points of S. Then

there exists a compact Hausdorff space Sx and a one-to-one embedding of S as

a dense subset of St such that each f in 21 has a

...

... Theorem 18, that the functions of 21 distinguish between the points of S. Then

there exists a compact Hausdorff space Sx and a one-to-one embedding of S as

a dense subset of St such that each f in 21 has a

**unique**continuous extension f-y...

Page 516

<f>^f>iS, s e S, <f>v ^ 6 G. Show that there is a countably additive non-negative

measure defined on the Borel sets of S which is not identically zero and is ^-

invariant for every <f> e G. 42 Show that in Exercise 38 the set function fx is

<f>^f>iS, s e S, <f>v ^ 6 G. Show that there is a countably additive non-negative

measure defined on the Borel sets of S which is not identically zero and is ^-

invariant for every <f> e G. 42 Show that in Exercise 38 the set function fx is

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed linear manifold compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations Doklady Akad element equivalent everywhere exists extended real valued extension fi(E finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality integral interval Lebesgue measure Lemma linear functional linear map linear operator linear topological space LP(S measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space uniformly unique v(fi valued function Vber vector valued weakly compact zero