## Linear Operators: General theory |

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Page 341

Show that a set K C ba(S, E) is conditionally compact if and only if (i) K is

bounded. ... 22 Let 5 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 ba(S, E) is conditionally compact if and only if (i) K is

bounded. ... 22 Let 5 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) rca(S)is weakly ...

Page 492

In the following, 08 denotes the field of

by the closed sets of S. If fj, is a function on 8S with values in a B-space, then as

in Definition IV. 10.8, the symbol denotes the semi-variation of fi over E e 88 and

...

In the following, 08 denotes the field of

**Borel sets**in S, i.e., the <r-field generatedby the closed sets of S. If fj, is a function on 8S with values in a B-space, then as

in Definition IV. 10.8, the symbol denotes the semi-variation of fi over E e 88 and

...

Page 516

39 Let S be a compact Hausdorff space and <f> a continuous function on S to S.

Show that there is a regular countably additive non-negative measure fi defined

for all

39 Let S be a compact Hausdorff space and <f> a continuous function on S to S.

Show that there is a regular countably additive non-negative measure fi defined

for all

**Borel sets**in S with the properties that fi is not identically zero and fi is ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed linear manifold compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations Doklady Akad element equivalent everywhere exists extended real valued extension fi(E finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality integral interval Lebesgue measure Lemma linear functional linear map linear operator linear topological space LP(S measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space uniformly unique v(fi valued function Vber vector valued weakly compact zero