## Linear Operators, Part 1 |

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Page 186

Thus the argument used in proving uniqueness in Lemma 1 goes through without

change in this case. Q.E.D. 3 DEFINITION. The

constructed in Theorem 2 is called the product

Thus the argument used in proving uniqueness in Lemma 1 goes through without

change in this case. Q.E.D. 3 DEFINITION. The

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

**measure space**of the**measure****spaces**...Page 188

Q.E.D. As in the case of finite

S, 2, u) constructed in Corollary 6 from ... known example of Theorem 2 and its

Corollary 6 is obtained by taking (S, X, u,) to be the Borel-Lebesgue measure on

...

Q.E.D. As in the case of finite

**measure spaces**we shall call the**measure space**(S, 2, u) constructed in Corollary 6 from ... known example of Theorem 2 and its

Corollary 6 is obtained by taking (S, X, u,) to be the Borel-Lebesgue measure on

...

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 positive

...

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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