## Linear Operators, Part 1 |

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Page 144

By our previous construction, we have already assigned a non-negative measure

u to every bounded

every

)} ...

By our previous construction, we have already assigned a non-negative measure

u to every bounded

**Borel set**B. Let I, - {s-n - s - +m}, and put u(B) ,, ... u(I,B) forevery

**Borel set**(the limit exists as an extended positive real number, since {u (I,B)} ...

Page 341

Show that a set K C bass, 2) is conditionally compact if and only if (i) K is

bounded. ... 22 Let S be a normal topological space and rca(S) the regular

countably additive set functions on the field of

is weakly ...

Show that a set K C bass, 2) is conditionally compact if and only if (i) K is

bounded. ... 22 Let S be a normal topological space and rca(S) the regular

countably additive set functions on the field of

**Borel sets**in S. Prove that (i) rea(S)is weakly ...

Page 634

Since p(E) is open if E is open, it follows immediately that p(E) is a

a

11.9), we have s". s". X,E) (s,t)ds dt = s". s". XE (s—t)dsdt = || || "... ze(s—t)ds at = s.

Since p(E) is open if E is open, it follows immediately that p(E) is a

**Borel set**if E isa

**Borel set**. Now let E be a**Borel set**of measure zero. By Fubini's theorem (III.11.9), we have s". s". X,E) (s,t)ds dt = s". s". XE (s—t)dsdt = || || "... ze(s—t)ds at = s.

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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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