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  • Title
  • CERTIFICATE
  • DECLARATION
  • ACKNOWLEDGEMENT
  • CONTENTS
  • Introduction
  • I. Fuzzy Total Variation
  • 1.0 Introduction
  • 1.1 Preliminaries
  • 1.2 Fuzzy Total Variation
  • 1.3 Fuzzy Upper Variation and Fuzzy Lower Variation
  • 1.4 Fuzzy ยต-null Function
  • 1.5 The Space F (Xp)
  • II. Integration of Fuzzy Simple Functions
  • 2.0 Introduction
  • 2.1 The Fuzzy Integrability
  • 2.2 Fuzzy Linear Subspace
  • III. Fuzzy Integrable Functions
  • 3.0 Introduction
  • 3.1 Fuzzy Integrable Function
  • IV. Some Important Theorems
  • 4.0 Introduction
  • 4.1 Countably Additive Fuzzy Measure
  • 4.2 Fuzzy Analogous forms of Egoroffs Theorem, Fatous Lemma and Dominated Convergence Theorem
  • V. Lebesgue Decomposition With Respect to a Fuzzy Measure
  • 5.0 Introduction
  • 5.1 Preliminaries
  • 5.2 Lebesgue Decomposition with Respect to a Fuzzy Measure.
  • VI. Fuzzy Vector Valued Integration
  • 6.0 Introduction
  • 6.1 The Fuzzy Semi-Variation of Fuzzy Vector Valued Measure.
  • 6.2 Integration with Respect to Fuzzy Vector Valued Measure
  • References