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Probabilistic normed spaces /
This book provides a comprehensive foundation in Probabilistic Normed (PN) spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A.N. Serstnev in the earl...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hackensack, NJ :
Imperial College Press,
[2014]
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Preliminaries. 1.1. Probability spaces. 1.2. Distribution functions. 1.3. The space of distance of distribution functions. 1.4. Copulas. 1.5. Triangular norms. 1.6. Triangle functions. 1.7. Multiplications. 1.8. Probabilistic metric spaces. 1.9. L[symbol] and Orlicz spaces. 1.10. Domination. 1.11. Duality
- 2. Probabilistic Normed spaces. 2.1. Probabilistic Normed spaces. 2.2. 1993: PN spaces redefined. 2.3. Special classes of PN spaces. 2.4. [symbol]-simple spaces. 2.5. EN spaces. 2.6. Probabilistic inner product spaces. 2.7. Open questions
- 3. The topology of PN spaces. 3.1. The topology of a PN space. 3.2. The uniform continuity of the probabilistic norm. 3.3. A PN space as a topological vector space. 3.4. Completion of PN spaces. 3.5. Probabilistic metrization of generalized topologies. 3.6. TIGT induced by probabilistic norms
- 4. Probabilistic norms and convergence. 4.1. The L[symbol] and Orlicz norms. 4.2. Convergence of random variables
- 5. Products and quotients of PN spaces. 5.1. Finite products. 5.2. Countable products of PN spaces. 5.3. Final considerations. 5.4. Quotients
- 6. D-boundedness and D-compactness. 6.1. The probabilistic radius. 6.2. Boundedness in PN spaces. 6.3. Total boundedness. 6.4. D-compact sets in PN spaces. 6.5. Finite dimensional PN spaces
- 7. Normability. 7.1. Normability of Serstnev spaces. 7.2. Other cases. 7.3. Normability of PN spaces. 7.4. Open questions
- 8. Invariant and semi-invariant PN spaces. 8.1. Invariance and semi-invariance. 8.2. New class of PN spaces. 8.3. Open questions
- 9. Linear operators. 9.1. Boundedness of linear operators. 9.2. Classes of linear operators. 9.3. Probabilistic norms for linear operators. 9.4. Completeness results. 9.5. Families of linear operators
- 10. Stability of some functional equations in PN spaces. 10.1. Mouchtari-Serstnev theorem. 10.2. Stability of a functional equation in PN spaces. 10.3. The additive Cauchy functional equation in RN spaces: Stability. 10.4. Stability in the quartic functional equation in RN spaces. 10.5. A functional equation in Menger PN spaces
- 11. Menger's 2-probabilistic Normed spaces. 11.1. Accretive operators in 2-PN spaces. 11.2. Convex sets in 2-PN spaces. 11.3. Compactness and boundedness in 2-PN spaces. 11.4. D-boundedness in 2-PN spaces.