I've got observed data $Y_1,\ldots, Y_n $ which consists of real values $X_1,\ldots, X_n$ and additive high-frequency noise $e_1,\ldots, e_n$, so $Y_i=X_i+e_i$. I know, that indices $i_1,\ldots, i_m, m<n$, refer to those samples in which $e_j=0$ if $j\in(i_1,\ldots,i_m)$.
I'm trying to implemen...0
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compact set always contains its supremum and infimum
People ask if compact set always contains its supremum and infimum. I know that it is true on $\mathbb{R}$ with the usual topology.
Pf: Let $K\subseteq \mathbb{R}$ be a nonempty compact set. Suppose not, by Heine Borel $K$ ...
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A search result for Mean Value Theorem gives us 2715 results, and results on the page are like ones I think we can include in the tag. The theorem is an important result in calculus, and questions relating to its applications, proofs. I think it would be useful if could have the tag, as it can gr...
