## Linear Operators, Part 1 |

### From inside the book

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Page 186

Thus, the field (p of Lemma I is a g-field and the measure u of Lemma I is

countably additive on p. Consequently, the ... Let (S, X, u) be the product of finite

So the ...

Thus, the field (p of Lemma I is a g-field and the measure u of Lemma I is

countably additive on p. Consequently, the ... Let (S, X, u) be the product of finite

**positive measure spaces**(S1, 21, ul) and (S2, 22, us). For each E in 2 and so inSo the ...

Page 302

Let (S, 2, u) be a

Lp(S, 2, u), 1 < p < 00, is a complete lattice. PRoof. It is evidently sufficient to

show that if {f.} is a set of functions in Li such that 0 < f, s go for some goe L.1,

then sup ...

Let (S, 2, u) be a

**positive measure space**. Then the real partially ordered spaceLp(S, 2, u), 1 < p < 00, is a complete lattice. PRoof. It is evidently sufficient to

show that if {f.} is a set of functions in Li such that 0 < f, s go for some goe L.1,

then sup ...

Page 725

n—1 lim sup I. X. u(q-'e) < Ku(e) n—-co "joo for each set e of finite u-measure. (

Hint. Consider the map f(s) → X1(s)f(ps) for each A e 2 with u(A) < 00.) 37 Let (S.

2, u) be a

...

n—1 lim sup I. X. u(q-'e) < Ku(e) n—-co "joo for each set e of finite u-measure. (

Hint. Consider the map f(s) → X1(s)f(ps) for each A e 2 with u(A) < 00.) 37 Let (S.

2, u) be a

**positive measure space**, and T a non-negative linear transformation of...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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