Lema lui Sard

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Cezar Lupu
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Lema lui Sard

Post by Cezar Lupu »

Fie \( g:[a, b]\to\mathbb{R} \) o functie derivabila cu derivata continua. Sa se arate ca multimea \( g(A) \), unde \( A=\{ x\in [a, b], g^{\prime} (x)=0 \} \), este neglijabila Lebesgue.
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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Iulian Cimpean
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Post by Iulian Cimpean »

Mai general, fie \( f: A \to R, A\subset R^{n}, A=\AA, \) f diferentiabila cu diferentiala continua. Atunci \( f(\{x \in A|J_f(x)=0\}) \) este neglijabila Lebesgue, si mai mult, urma sa pe o multime marginita e masurabila Jordan.
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