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Results tagged with real-analysis
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user 70686
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
8
votes
2
answers
889
views
Differentiating an integral that grows like log asymptotically
Suppose I have a continuous function $f(x)$ that is non-increasing and always stays between $0$ and $1$, and it is known that
$$ \int_0^t f(x) dx = \log t + o(\log t), \qquad t \to \infty.$$
Unfortu …
- 205
10
votes
2
answers
340
views
A moment problem
Suppose $X, Y$ are two positive random variables such that $\mathbb{E}[X^\alpha] = \mathbb{E}[Y^\alpha]$ for all $\alpha \in (0, 1/2)$.
It is also known that the first moment exists for each of them, …
- 205