## Linear Operators: General theory |

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Page 4

If A is an infinite set of real numbers, then the symbol lim sup A

infimum of all numbers b with the property that only a finite set of numbers in A

exceed b; the definition of the symbol lim inf A is similar. In particular, if A is a

sequence ...

If A is an infinite set of real numbers, then the symbol lim sup A

**denotes**theinfimum of all numbers b with the property that only a finite set of numbers in A

exceed b; the definition of the symbol lim inf A is similar. In particular, if A is a

sequence ...

Page 103

For an example of such a function, let S = [0, 1 ) and Z be the field of finite unions

of intervals / = [a, b), 0 ^ a < b < 1, with u(I) = b—a as in Section 1. Let R

the set of rational points in S. For r = p/q e R in lowest terms, we define F(pjq) = \jq

, ...

For an example of such a function, let S = [0, 1 ) and Z be the field of finite unions

of intervals / = [a, b), 0 ^ a < b < 1, with u(I) = b—a as in Section 1. Let R

**denote**the set of rational points in S. For r = p/q e R in lowest terms, we define F(pjq) = \jq

, ...

Page 142

Throughout the proof the symbol E with or without subscripts will

, the symbol M with or without subscripts will

0, and A" with or without subscripts will

Throughout the proof the symbol E with or without subscripts will

**denote**a set in Z, the symbol M with or without subscripts will

**denote**a set in Z for which v(fi, M) =0, and A" with or without subscripts will

**denote**a subset of a set M. To see that ...### 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