Lebesgue’s Theorem (see below) has been called one of the most striking theorems in real analysis. Indeed it is a very surprising result. Lebesgue’s Theorem (Monotone functions) If the function is monotone on the open interval , then it is differentiable almost everywhere on . Absolutely Continuous Functions Definition A real-valued function on a closed, […]

via The most Striking Theorem in Real Analysis — Singapore Maths Tuition

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