## Linear Operators: General theory |

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Page 143

Then the function // with domain Z* is known as the

The a-field Z* is known as the

and the

space ...

Then the function // with domain Z* is known as the

**Lebesgue**extension of /u.The a-field Z* is known as the

**Lebesgue**extension {relative to /u) of the tx-field Z,and the

**measure**space (S, Z*, fi) is the**Lebesgue**extension of the**measure**space ...

Page 188

The best known example of Theorem 2 and its Corollary 6 is obtained by taking (

5„ Eit fa) to be the Borel-

S = Pf=1 S{ is w-dimensional Euclidean space, and fi = fa X . . . X (in is known as

...

The best known example of Theorem 2 and its Corollary 6 is obtained by taking (

5„ Eit fa) to be the Borel-

**Lebesgue measure**on the real line for i = 1, . . ., n. ThenS = Pf=1 S{ is w-dimensional Euclidean space, and fi = fa X . . . X (in is known as

...

Page 223

Show that the Lebesgue-Stieltjes integral jdeg(f(s))dh{f(8)) exists and is equal to I

. 6 Show that a monotone increasing function / defined on an interval is

differentiable almost everywhere with respect to

may ...

Show that the Lebesgue-Stieltjes integral jdeg(f(s))dh{f(8)) exists and is equal to I

. 6 Show that a monotone increasing function / defined on an interval is

differentiable almost everywhere with respect to

**Lebesgue measure**and that /'may ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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