## Linear Operators, Part 1 |

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Page 125

By Theorem 7 , \ in - mello < E for

Functions The basis for the present III.3.8 125 LEBESGUE SPACES.

By Theorem 7 , \ in - mello < E for

**sufficiently**large n . Hence - tule < 2 € for**sufficiently**large n and the proof is complete . Q.E.D. 4. Countably Additive SetFunctions The basis for the present III.3.8 125 LEBESGUE SPACES.

Page 472

Šmulian [ 7 ] obtains two interesting necessary and

differentiability of the norm . THEOREM . In order that the norm is strongly

differentiable at a point æ in a B - space X , it is necessary and

every ...

Šmulian [ 7 ] obtains two interesting necessary and

**sufficient**conditions for strongdifferentiability of the norm . THEOREM . In order that the norm is strongly

differentiable at a point æ in a B - space X , it is necessary and

**sufficient**thatevery ...

Page 592

If 20 € D is such that T - 1 ( 2 ) exists , then it follows from Lemma 6 that for a

neighborhood of 2o . To prove the second part of the lemma we suppose that

there is ...

If 20 € D is such that T - 1 ( 2 ) exists , then it follows from Lemma 6 that for a

**sufficiently**near , the inverse T - 1 ( 2 ) exists and is an analytic function of 2 in aneighborhood of 2o . To prove the second part of the lemma we suppose that

there is ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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