Mathematical analysis. Consider a more specific tag instead: (real-analysis), (complex-analysis), (functional-analysis), (fourier-analysis), (measure-theory), (calculus-of-variations), etc. For data analysis, use (data-analysis).

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Why is it enough to prove the sentence?

I am looking at the proof of the theorem that for any rectangle the outer measure is equal to the volume. At the beginning of the proof there is the following sentence: It is enough to look at the ...
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Evaluating the limit for the Minkowski content of $F_{\alpha}=\{0,1,\frac{1}{2^{\alpha}},\frac{1}{3^{\alpha}},\frac{1}{4^{\alpha}},\dots\}$.

The Minkowski content is defined as $\displaystyle M_{\beta}(A)=\lim_{\delta \rightarrow 0} \frac{\mu(A_{\delta})}{(2\delta)^{1-\beta}}$ where $0 < \beta < 1$, $A \subset \mathbb{R}$, and ...
3
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1answer
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An asymptotic expression of sum of powers of binomial coefficients.

Let $k$ be a fixed positive number and $n$ an integer increasing to infinity. Then $$\sum_{\nu =0}^n \binom{n}{\nu}^k \sim \frac{2^{kn}}{\sqrt{k}} \left( \frac{2}{\pi n} \right)^{\frac{k-1}{2}}.$$ ...
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Find a compression of the frames over the subspaces

Find a compression of the frames $B=\{(1,1,0),(1,-1,0),(1,1,1),(0,0,1),(0,1,-1)\}$ over the subspaces (a) $M=\{(x,y,z):x=0\}$, (b) $M=\{(x,y,z):x=y\}$ Find an orthonormal basis $B$ of $\mathbb{R}^4$ ...