## Linear Operators: General theory |

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Page 168

Let ( S , E , u ) be a positive measure space and G a

, M , X ) , where 1 sp < 00 . Then there is a set S , in E , a sub o - field Ey of E ( S ) ,

and a closed

Let ( S , E , u ) be a positive measure space and G a

**separable**subset of L ( S , E, M , X ) , where 1 sp < 00 . Then there is a set S , in E , a sub o - field Ey of E ( S ) ,

and a closed

**separable**subspace X of % such that the restriction My of u to Ey ...Page 501

If the compact Hausdorff space S has a countable base the space C ( S ) is

space . If y ( x , y ) is a metric in S let 1n ( x ) = Q ( x , xn ) where { Xn } is a

denumerable ...

If the compact Hausdorff space S has a countable base the space C ( S ) is

**separable**. Proof . By Theorems 1 . 6 . 19 and 1 . 6 . 12 , S is a**separable**metricspace . If y ( x , y ) is a metric in S let 1n ( x ) = Q ( x , xn ) where { Xn } is a

denumerable ...

Page 507

may be noted that the next theorem applies to every continuous linear map of L (

S , E , u ) into a

finite positive measure space , and let T be a weakly compact operator on L ( S ...

may be noted that the next theorem applies to every continuous linear map of L (

S , E , u ) into a

**separable**reflexive space . 10 THEOREM . Let ( S , E , u ) be a o -finite positive measure space , and let T be a weakly compact operator on L ( S ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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