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New posts in monotone-functions
If $F$ is differentiable at $x_0$, $f$ is continuous at $x_0$
real-analysis
integration
derivatives
monotone-functions
Proof of Lebesgue Differentation Theorem in Lipschitz Analysis Lectures by Heinonen
real-analysis
analysis
monotone-functions
Let $f$ be increasing on $[a,b]$ and $a < x_1 < \dotsb < x_n < b$. Show that $\sum_{k = 1}^n [f(x_k^+) - f(x_k^-)]\leq f(b^-) - f(a^+)$.
real-analysis
calculus
inequality
monotone-functions
bounded-variation
Are Monotone functions Borel Measurable?
measure-theory
monotone-functions
measurable-functions
borel-sets
Prove that the function $ g $ satisfying $g(g(x))=2g(x)-x $ is strictly monotonic.
monotone-functions
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