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Page 460
... invariant if u ( sE ) u ( E ) for all se G , E. Such a measure is often called Haar measure . 23 ( Haar ) Let G be a ... invariant and is not identically zero , and that any two left - invariant measures differ only by a scalar factor ...
... invariant if u ( sE ) u ( E ) for all se G , E. Such a measure is often called Haar measure . 23 ( Haar ) Let G be a ... invariant and is not identically zero , and that any two left - invariant measures differ only by a scalar factor ...
Page 516
... invariant . 39 Let S be a compact Hausdorff space and a continuous function on S to S. Show that there is a regular countably additive non - negative measure μ defined for all Borel sets in S with the prop- erties that is not ...
... invariant . 39 Let S be a compact Hausdorff space and a continuous function on S to S. Show that there is a regular countably additive non - negative measure μ defined for all Borel sets in S with the prop- erties that is not ...
Page 847
... Invariant measures , V.11.22 ( 460 ) , VI.9.38-44 ( 516 ) Invariant metric , in a group , ( 90-91 ) in a linear space , II.1.10 ( 51 ) Invariant set , ( 3 ) Invariant subgroup , ( 35 ) Inverse function and inverse image , ( 3 ) Inverse ...
... Invariant measures , V.11.22 ( 460 ) , VI.9.38-44 ( 516 ) Invariant metric , in a group , ( 90-91 ) in a linear space , II.1.10 ( 51 ) Invariant set , ( 3 ) Invariant subgroup , ( 35 ) Inverse function and inverse image , ( 3 ) Inverse ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ