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This chapter summarises the key definitions and properties of capacities, giving the foundation and background required for subsequent chapters. A number of important capacity types are defined by restrictions on the general definition, which are presented along with contextual interpretations or applications. The consequent behaviour of Choquet or nonadditive integrals when defined with respect to these capacities is also noted.

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Types of Capacities

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  • 发表日期：

    2026年

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  • Gleb Beliakov,
  • Simon James,
  • Jianzhang Wu

摘要

This chapter summarises the key definitions and properties of capacities, giving the foundation and background required for subsequent chapters. A number of important capacity types are defined by restrictions on the general definition, which are presented along with contextual interpretations or applications. The consequent behaviour of Choquet or nonadditive integrals when defined with respect to these capacities is also noted.