mod12lec71 - Differentiation theorems: Almost everywhere differentiability for Monotone and Bounded

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DIfferentiation theorems: Almost everywhere differentiability for Monotone and Bounded Variation functions - Part 1

Monotonically non-decreasing functions, Functions of bounded variation (BV), Second fundamental theorem of Calculus, Examples and Non-examples of BV functions, BV functions as a difference of monotonically non-decreasing functions
  1. NPTEL-NOC IITM
  2. Measure Theory
  3. Prof. Indrava Roy
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You can prove the lemma in the following way as well. Consider the total variation T_f of f on [a, b] then it is easy to show that T_f + f and T_f - f are both increasing on [a, b] and note that f = 1/2 [(T_f + f) - (T_f - f)] and then we are done with the proof.

ACh