# All Questions

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### Physical meaning of the Lebesgue measure

Question (informal) Is there an empirically verifiable scientific experiment that can empirically confirm that the Lebesgue measure has physical meaning beyond what can be obtained using just the ...
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### Functional equation: Can we find a function that satisfies this equation?

$f^{\alpha }\left( \overrightarrow {0}\right) +f^{\beta }\left( \overrightarrow {0}\right) =f^{\alpha \beta +\alpha +\beta }\left( \overrightarrow {0}\right)$ Is there a function $f$ from ...
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### Proof of partial derivative of a distribution

I wanted to proof the formula for the partial derivative of a distribution, but I have an error on my result and I don't understand where I am wrong. Here is my proof : I assume that my function f ...
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### function space in comma category

Let TOP be a category of topological spaces and B be an object of TOP. Is there a notion of function space in the comma category TOP/B.
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### Is the functor of open subschemes representable?

First some simple observations in order to motivate the question: The functor $Set^{op} \to Set, X \to \{\text{subsets of }X\}, f \to (U \to f^{-1}(U))$ is representable. The representing object is ...
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### Passing motivic decompositions from rational to algebraic equivalence

It is well known that there are several adequate equivalence relations for algebraic cycle (see https://en.wikipedia.org/wiki/Adequate_equivalence_relation for a list including definitions). The ...
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### How to solve these simultaneous equations? [on hold]

Find the all possible pairs of $x,y,z$ so that 1) $y^3 = x^3 + 9x^2 - 9x +8$ 2) $y^2 = z^3 + 17$ Note that, $x,y,z$ are all positive integers. I've tried many ways to solve this problem but ...
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### significance level from 0.10 to 0.05, increase or decrease? [on hold]

A trend test show the trend is downward (alpha<0.10). Then the trend is still downward, but alpha<0.05. Then I describe as follows: 1. The statistical significance is increasing. 2. The ...
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### How to write the map $ℂ[G/U]↪ℂ[B]$ explicitly?

Let $G$ be a reductive algebraic group and $B$ a Borel subgroup of $G$. Let $T$ be a maximal torus of $G$ contained in $B$. The $B=UT=TU$ for some unipotent subgroup $U$ of $G$. We have Bruhat ...
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### Points of failure in definition of X- and A-moduli spaces for arbitrary G

In their work [0] on defining notions of higher Teichmüller space for local systems on surfaces, Fock and Goncharov require split reductive Lie groups, and sometimes also require simple-connectedness. ...