## Linear Operators: General theory |

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Page 106

The

on S are the

every E in E with v(u, E) < oo, the product %Ef °f / with the characteristic

The

**functions**totally u-**measurable**on S, or, if // is understood, totally**measurable**on S are the

**functions**in the closure TM(S) in F(S) of the //-simple**functions**. If forevery E in E with v(u, E) < oo, the product %Ef °f / with the characteristic

**function**...Page 179

Let (S, Z, p) be a positive measure space, f a non- negative (i-

s)g(s)/i(ds), ...

Let (S, Z, p) be a positive measure space, f a non- negative (i-

**measurable****function**defined on S and X(E)=jBf(s)/l{ds), EeZ. Let g be a non-negative X-**measurable function**defined on S. Then fg is /^-measurable, and jEg(s)X(ds)=jEf(s)g(s)/i(ds), ...

Page 180

Since every real

(ds), E e Z, for a real

a ...

Since every real

**measurable function**is the difference of two non- negative**measurable functions**, it follows from the theorem that [*] jE g(s)Hcb) = j£ f(S)g(s)fi(ds), E e Z, for a real

**measurable function**g. Since the real and imaginary parts ofa ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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