First Sentence:
In this chapter we present some definitions, notations, and preliminary results that are used throughout the present work.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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symmetric derivates, unilateral derivates, generalized derivates, derivability sets, strong derivates, typical continuous functions, nonmeager set, nonderivable functions, derivability hypothesis, derivability theorem, ordinary derivability, derivate theorem, approximate derivates, ordinary derivates, following monotonicity theorem, den vates, nowhere monotone functions, knotted function, knotted lower derivatives, strong derivability, lower singular, new derivability, lower knotted, congruent derivative, unilateral derivatives
Key Phrases - Capitalized Phrases (CAPs):
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First Derivate Theorem, Third Derivate Theorem, Second Mean Value Theorem, First Derivability Theorem, Status Theorems, Third Derivability Theorem, Second Monotonicity Theorem, Second Derivability Theorem, Fifth Derivate Theorem, Third Median Theorem, Fifth Derivability Theorem, Fourth Monotonicity Theorem, Second Status Theorem, Third Monotonicity Theorem, Fourth Derivability Theorem, Fifth Status Theorem, First Monotonicity Theorem, Morse's Theorem, Second Median Theorem, First Induction Theorem, Fourth Median Theorem, H-admissible H-derivates, Seventh Status Theorem, Third Induction Theorem, Third Status Theorem
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