## Linear Operators: General theory |

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Page 186

Thus, the field 0 of Lemma 1 is a a-f ield and the measure /i of Lemma 1 is

countably additive on 0. ... The

is called the product

In ...

Thus, the field 0 of Lemma 1 is a a-f ield and the measure /i of Lemma 1 is

countably additive on 0. ... The

**measure space**(S, E, u) constructed in Theorem 2is called the product

**measure space**of the**measure spaces**(S„, En, un). We writeIn ...

Page 405

sional Gauss

real sequences x = \x{\ as distinct from l2, which is the subspace of * determined

by the condition < oo. The

...

sional Gauss

**measure**on the real line. The**space**s is, of course, the**space**of allreal sequences x = \x{\ as distinct from l2, which is the subspace of * determined

by the condition < oo. The

**measure**it^ is countably additive; the subset ^ of * is of...

Page 725

I n-1 lim sup - 2 iM(99_'e) Knie) fl-*00 11 ;=0 for each set e of finite ^-measure. (

Hint. Consider the map f(s) -> xA(s)f((ps) for each ^4 e27 with < oo.) 87 Let (5, 2",

// ) be a positive

I n-1 lim sup - 2 iM(99_'e) Knie) fl-*00 11 ;=0 for each set e of finite ^-measure. (

Hint. Consider the map f(s) -> xA(s)f((ps) for each ^4 e27 with < oo.) 87 Let (5, 2",

// ) be a positive

**measure space**, and T a non-negative linear transformation of ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### 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 compact operator complex numbers complex valued contains continuous functions continuous linear convex set Corollary countably additive Definition denote dense differential equations disjoint sets Doklady Akad Duke Math element equivalent everywhere exists extended real valued extension finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality interval Lebesgue measure lim sup linear functional 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 Proof properties proved real numbers Riesz Russian semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space Trans uniformly unique v(fi valued function Vber vector valued weakly compact