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Results tagged with real-analysis
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user 133871
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
10
votes
1
answer
1k
views
Is there a strictly increasing differentiable function maps positively measurable set to zer...
Let $g(t)$ be a strictly increasing differentiable function. Can it map positively measurable set to zero measurable set?
It's obviously that $\{g'>0\}$ is dense. If I can prove that the Lebesgue mea …
- 2,437
2
votes
1
answer
423
views
If $\int_E f = 0$ for all $E$ the translation and dilation of $E_0$ then $f = 0 \text{ } a.e.$
Let $f \in L^1(\mathbb{R}^n)$. It's obvious that if $\int_R f = 0$ for all rectangles $R$ then $f = 0$ $a.e.$ since every open set is union of almost disjoint rectangles and consequently with zero in …
- 17.2k