## Linear Operators, Part 1 |

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Page 103

space of all functions which map S into 3 (see I.6.1). Unfortunately, this is rarely

the case and so a slight detour will be made. 3 DEFINITION. The

to 3 is said to be a u-null function or, when u is understood, simply a null function

if ...

space of all functions which map S into 3 (see I.6.1). Unfortunately, this is rarely

the case and so a slight detour will be made. 3 DEFINITION. The

**function f**on Sto 3 is said to be a u-null function or, when u is understood, simply a null function

if ...

Page 196

For each s in S, F(s) is an equivalence class of functions, any pair of whose

members coincide A-almost everywhere. If for each s we select a particular

× (T, 21, ...

For each s in S, F(s) is an equivalence class of functions, any pair of whose

members coincide A-almost everywhere. If for each s we select a particular

**function f**(s, -) e F(s), the resulting**function f**(s, t) defined on (R, 2r, 9) = (S, As. Au)× (T, 21, ...

Page 199

integral ss

. 2 r. 2, 3). PRoof. Let Xr be partitioned into a sequence {E,} of disjoint sets of finite

Z-measure. For 1 < p < 20 let L, H Lp(T. 2 r, 2, 3) and define the maps U, n = 1, ...

integral ss

**f**(s,t)a(ds), as a**function**of t, is equal to the element Js**F**(s) u(ds) of L,(T. 2 r. 2, 3). PRoof. Let Xr be partitioned into a sequence {E,} of disjoint sets of finite

Z-measure. For 1 < p < 20 let L, H Lp(T. 2 r, 2, 3) and define the maps U, n = 1, ...

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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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