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E-grāmata: Selected Topics of an Infinite-Dimensional Classical Analysis

  • Formāts: 195 pages
  • Izdošanas datums: 01-Apr-2014
  • Izdevniecība: Nova Science Publishers Inc
  • ISBN-13: 9781619427181
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Selected Topics of an Infinite-Dimensional Classical AnalysisPalielināt
  • Formāts: 195 pages
  • Izdošanas datums: 01-Apr-2014
  • Izdevniecība: Nova Science Publishers Inc
  • ISBN-13: 9781619427181
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This book explores a new concept of T-shy sets in Radon metric groups which is an extension of the concepts of null sets introduced by J.R. Christensen, J. Mycielski and B. R. Hunt, T. Sauer and J. A. Yorke for Polish groups. This book considers various interesting applications of the theory of infinite-dimensional cellular matrices for a solution of various initial condition problems. It also includes several direct generalizations of well-known classical results (Lebesgue theorem, Weyl theorem, Rademacher theorem, etc) in terms of infinite-dimensional "e;Lebesgue measures"e;.
Introduction ix
1 On Witsenhausen-Kalai constants for surface measures on a sphere
1(16)
1.1 Introduction
1(4)
1.2 On Question 1.1.2
5(3)
1.3 On Frankl-Wilson result
8(1)
1.4 On a certain geometric inequality on a sphere Sn
9(3)
1.5 On Witsenhausen-Kalai constants for Gaussian surface measure on an infinite-dimensional unite sphere S∞
12(5)
2 On strict standard and strict ordinary products of measures and some of their applications
17(34)
2.1 Introduction
17(1)
2.2 An Auxiliary Lemma
18(7)
2.3 On strict ordinary and standard products of infinite family of σ-finite measures
25(12)
2.4 On a strict standard product of an arbitrary family of σ-finite Borel measures with domain in Polish spaces
37(6)
2.5 Some auxiliary propositions in Solovay model
43(1)
2.6 On infinite versions of Rademacher theorem for R∞ in Solovay model
44(3)
2.7 On uniform measures on lα
47(1)
2.8 On a completion of the B(R∞) by the Baker measure
48(3)
3 On invariant extensions of the strict standard product of Haar measures with domains in Polish groups
51(12)
3.1 Introduction
51(1)
3.2 Invariant extensions of the strict standard product of Haar measures
52(8)
3.3 On uniform measures on lα
60(3)
4 An expansion into an infinite-dimensional multiple trigonometric series of a square integrable function in R∞
63(10)
4.1 Introduction
63(1)
4.2 Auxiliary propositions
64(5)
4.3 Main Results
69(4)
5 On uniformly distributed sequences of an increasing family of finite sets in infinite-dimensional rectangles
73(14)
5.1 Introduction
73(1)
5.2 Auxiliary notions and propositions
74(1)
5.3 On uniformly distributed sequences of increasing family of finite sets in infinite-dimensional rectangles
75(10)
5.4 On uniformly distribution in infinite-dimensional rectangles
85(2)
6 On some applications of infinite-dimensional cellular matrices
87(24)
6.1 Introduction
87(1)
6.2 Some auxiliary notions and facts
87(4)
6.3 Formulations and proofs of main results
91(11)
6.4 Observations
102(1)
6.5 On phase flows in R∞ defined by Riemann's alternating zeta function
103(4)
6.6 On a heat equation for a function of n-spatial variables
107(4)
7 On singularity of non-σ-finite measures and transition kernels
111(14)
7.1 Introduction
111(1)
7.2 Some axioms of the set theory
112(2)
7.3 On a mutually singularity for non-σ finite measures
114(5)
7.4 Orthogonal transition kernels
119(6)
8 On separation problem for the family of Borel and Baire G-powers of shift-measures on R
125(12)
8.1 Introduction
125(1)
8.2 Some auxiliary notions and facts
126(7)
8.3 Formulations and proofs of main results
133(4)
9 On T-Shy sets in Radon metric groups
137(22)
9.1 Introduction
137(1)
9.2 Relation between invariance and quasi-invariance for Borel probability measures in Radon metric spaces
138(4)
9.3 On T-cm and T-shy sets in complete metric groups
142(5)
9.4 On generators of (T, μ)-shy sets in complete metric groups
147(3)
9.5 On quasi-finiteness of the generator of (π(V), μ)-shy sets in a Polish topological vector space V
150(4)
9.6 On a certain example of T-cm and T-shy sets in R∞
154(1)
9.7 On a certain application of Corollary 9.3.1
155(4)
10 On an equivalence of outer measures and measures on Polish spaces
159(6)
10.1 Introduction
159(1)
10.2 Some auxiliary notions and propositions
160(2)
10.3 Main result
162(3)
References 165(16)
Index 181
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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