Abstract
In this chapter we introduce selected limit theorems on fuzzy quantum space, namely Egorov’s theorem, Central limit theorem, Weak and strong law of large numbers, and extreme value theorems for fuzzy quantum space. We also study here the Ergodic theory for fuzzy quantum space and Ergodic theorems and Poincaré recurrence theorems for fuzzy quantum dynamical systems, the Hahn-Jordan decomposition and Lebesgue decomposition for fuzzy quantum space.
Keywords: Egorov’s theorem, Central limit theorem, Weak law of large numbers, Strong law of large numbers, Fisher-Tippett, Gnedenko theorem, Balkema, de Haan-Pickands theorem, Birkhoff’s individual ergodic theorem, The representation theorem, Individual Ergodic Theorem, Poincaré recurrence theorem, Strong Poincaré recurrence theorem, Hahn-Jordan decomposition, Lebesgue decomposition.
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