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Category Archives: Analysis
A Eulogy Of Lipschitz Maps
A Lipschitz map (/function) is one that does not extend distances by more than a preassigned factor: $f: X \longrightarrow Y$ is Lipschitz if there exists an $L \in \mathbb{R}$ such that $$ \forall x, \ \ \forall y \ … Continue reading
Posted in Analysis, Math
Tagged Change of Variables, Lipschitz Maps, Luzin N Property, Radamacher's Theorem
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Intersection of a Chain of Subsets
Assume $\{F_x\}_{x \in \Gamma}$ is a collection of subsets (of a notso important set!) such that every two are comparable, i.e for any $x$ and $y$, either $F_x \subset F_y \ \ $ or $\ \ F_x \supset F_y \ … Continue reading