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Let $(Omega,mathcal A,mu)$ be a $sigma$-finite measure space, $pge1$, $E_i$ be a $mathbb R$-Banach space, $U_1subseteq E_1$ be open and $f:U_1to L$ be...

Asked on 12/27/2021

0Let $u_m = ln ^2 m$.Does there exist a non-increasing sequence of positive numbers ${g_n}_{n in mathbb{N}}$, $g_n to 0$, such that $$sumlimits_{n in mathbb{N}...

Asked on 12/27/2021

1Let $R$ be a commutative ring with characteristic $0$, namely it contains the field of rational numbers. Higher Algebra Proposition 7.1.4.10 tells that the category...

Asked on 12/27/2021 by Francesco Genovese

2Let $L$ be a finite lattice and $x in L$ with covers $r_1,...,r_l$ in $L$. One can define $row(x):= min { y | y leq...

Asked on 12/27/2021

0Is it true that every nonzero endomorphism of Lie $mathbb{C}$-algebra $mathbb{C}[x_1,ldots, x_n]partial_{x_1}oplusldotsoplusmathbb{C}[x_1,ldots, x_n]partial_{x_n}$ is an automorphism?As I know a positive answer to question implies the Jacobian conjecture for...

Asked on 12/25/2021

0$D_ntriangleq left{x in mathbb{R}^n:, |x|leq 1right}$ with its subspace topology. By a transitive flow on $D_n$ I mean a continuous function$$phi: [0,1]times D_nrightarrow D_n,...

Asked on 12/25/2021

1Let ${cal U}$ be a non-principal ultrafilter on $omega$, and for each $ninomega$, let $p_n$ denote the $n$th prime, that is $p_0 = 2,...

Asked on 12/25/2021

2The question. Which mathematical objects would you like to see formally defined in the Lean Theorem Prover? Examples. In the current stable version of the Lean Theorem...

Asked on 12/21/2021 by Kevin Buzzard

28Here is the question. Does the Riemann Xi function possess the universality property, or something similar to Voronin's universality property? Here is why the answer to this question is...

Asked on 12/21/2021

1Suppose we have $n$ ordered realizations of a random variable uniformly distributed over the unit cube $P = (p_1, p_2, cdots, p_n), p_i in [0,1]^d $. And we...

Asked on 12/21/2021 by yupbank

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