# Tagged Questions

Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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### Relative null-ness

Here, "measure" always means Lebesgue measure on $\mathbb{R}$. This question is partly motivated by my answer http://math.stackexchange.com/questions/1444498/is-there-a-categorizaiton-system-for-null-...
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### A question about small sets of reals

In ZFC, does there exist an uncountable set of reals $A$ such that for every closed measure zero set of reals $B$, we have that $A + B = \{a+b : a \in A, b \in B\} \neq \mathbb{R}$? This question is ...
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### Concept associated to the Eudoxus reals

I am aware of three different constructions of the field of real numbers : The Cauchy sequence construction : in this case, we see the field $\mathbb{Q}$ as a metric space and $\mathbb{R}$ is the ...
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### Classes of (non-continuous) functions with the fixed point property

Let $K$ be a convex body in $R^d$. (Say, a ball, say a cube...) For which classes $\cal C$ of functions, every function $f \in {\cal C}$ which takes $K$ into itself admits a fixed point in $K$. ...
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Let $\Delta(s_1,s_2,\ldots,s_n) = \prod_{i<j}(s_i-s_j)^2$. Is there a standard way to estimate the decay of the Selberg-type integral $$\frac{1}{n!^2}\int_0^1 \int_0^1\cdots\int_0^1 \frac{\Delta(... 0answers 326 views ### A multiple integral Let us consider the multiple integral$$I_{n}=\int_{-\infty }^{\infty }ds_{1}\int_{-\infty}^{s_{1}}ds_{2}\cdots \int_{-\infty }^{s_{2n-1}}ds_{2n}\;\cos {(s_{1}^{2}-s_{2}^{2})}\;\cdots \cos {(s_{2n-1}...
This might be very trivial, or not. Let $p\colon\mathbb{R}^n\to \mathbb{R}$ be a polynomial of even degree, at most $n-2$. Assume that $p(x)\leq 0$ for any $x\in\mathbb{R}^n$. Assume that there ...