Less than $2^{ω}$ many translates of a compact nullset may cover the real line

Márton Elekes; Juris Steprāns

Displaying similar documents to “Less than $2^{ω}$ many translates of a compact nullset may cover the real line”

Monotonically normal $e$ -separable spaces may not be perfect

John E. Porter (2018)

Commentationes Mathematicae Universitatis Carolinae

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A topological space $X$ is said to be $e$ -separable if $X$ has a $σ$ -closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that $e$ -separable PIGO spaces are perfect and asked if $e$ -separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of $e$ -separable monotonically normal spaces which are not perfect. Extremely normal $e$ -separable spaces are shown to be stratifiable.

On Peano derivatives in $L^{p} (E_{n})$

S. Lasher (1968)

Studia Mathematica

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A new Lindelöf space with points $G_{δ}$

Alan S. Dow (2015)

Commentationes Mathematicae Universitatis Carolinae

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We prove that $♦^{*}$ implies there is a zero-dimensional Hausdorff Lindelöf space of cardinality $2^{ℵ_{1}}$ which has points $G_{δ}$ . In addition, this space has the property that it need not be Lindelöf after countably closed forcing.

Characteristic points, rectifiability and perimeter measure on stratified groups

Valentino Magnani (2006)

Journal of the European Mathematical Society

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We establish an explicit connection between the perimeter measure of an open set $E$ with $C^{1}$ boundary and the spherical Hausdorff measure $S^{Q - 1}$ restricted to $\partial E$ , when the ambient space is a stratified group endowed with a left invariant sub-Riemannian metric and $Q$ denotes the Hausdorff dimension of the group. Our formula implies that the perimeter measure of $E$ is less than or equal to $S^{Q - 1} (\partial E)$ up to a dimensional factor. The validity of this estimate positively answers a conjecture raised by Danielli,...

Relations between Shy Sets and Sets of $ν_{p}$ -Measure Zero in Solovay’s Model

G. Pantsulaia (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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An example of a non-zero non-atomic translation-invariant Borel measure $ν_{p}$ on the Banach space $ℓ_{p} (1 \leq p \leq \infty)$ is constructed in Solovay’s model. It is established that, for 1 ≤ p < ∞, the condition " $ν_{p}$ -almost every element of $ℓ_{p}$ has a property P" implies that “almost every” element of $ℓ_{p}$ (in the sense of [4]) has the property P. It is also shown that the converse is not valid.

Approximate and $L^{p}$ Peano derivatives of nonintegral order

J. Marshall Ash, Hajrudin Fejzić (2005)

Studia Mathematica

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Let n be a nonnegative integer and let u ∈ (n,n+1]. We say that f is u-times Peano bounded in the approximate (resp. $L^{p}$ , 1 ≤ p ≤ ∞) sense at $x \in ℝ^{m}$ if there are numbers $f_{α} (x)$ , |α| ≤ n, such that $f (x + h) - \sum_{| α | \leq n} f_{α} (x) h^{α} / α!$ is $O (h^{u})$ in the approximate (resp. $L^{p}$ ) sense as h → 0. Suppose f is u-times Peano bounded in either the approximate or $L^{p}$ sense at each point of a bounded measurable set E. Then for every ε > 0 there is a perfect set Π ⊂ E and a smooth function g such that the Lebesgue measure of E∖Π is less than ε and...

Characterizations of $z$ -Lindelöf spaces

Ahmad Al-Omari, Takashi Noiri (2017)

Archivum Mathematicum

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A topological space $(X, τ)$ is said to be $z$ -Lindelöf [1] if every cover of $X$ by cozero sets of $(X, τ)$ admits a countable subcover. In this paper, we obtain new characterizations and preservation theorems of $z$ -Lindelöf spaces.

On starshapedness of the union of closed sets in $R^{n}$

Krzysztof Kołodziejczyk (1987)

Colloquium Mathematicae

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On hereditary normality of $ω^{*}$ , Kunen points and character $ω_{1}$

Sergei Logunov (2021)

Commentationes Mathematicae Universitatis Carolinae

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We show that $ω^{*} ∖ {p}$ is not normal, if $p$ is a limit point of some countable subset of $ω^{*}$ , consisting of points of character $ω_{1}$ . Moreover, such a point $p$ is a Kunen point and a super Kunen point.

Generalized Lebesgue points for Sobolev functions

Nijjwal Karak (2017)

Czechoslovak Mathematical Journal

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In many recent articles, medians have been used as a replacement of integral averages when the function fails to be locally integrable. A point $x$ in a metric measure space $(X, d, μ)$ is called a generalized Lebesgue point of a measurable function $f$ if the medians of $f$ over the balls $B (x, r)$ converge to $f (x)$ when $r$ converges to $0$ . We know that almost every point of a measurable, almost everywhere finite function is a generalized Lebesgue point and the same is true for every point of a continuous function....

Extensions of generic measure-preserving actions

Julien Melleray (2014)

Annales de l’institut Fourier

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We show that, whenever $Γ$ is a countable abelian group and $Δ$ is a finitely-generated subgroup of $Γ$ , a generic measure-preserving action of $Δ$ on a standard atomless probability space $(X, μ)$ extends to a free measure-preserving action of $Γ$ on $(X, μ)$ . This extends a result of Ageev, corresponding to the case when $Δ$ is infinite cyclic.

On decomposability of finite groups

Ruifang Chen, Xianhe Zhao (2017)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group. A normal subgroup $N$ of $G$ is a union of several $G$ -conjugacy classes, and it is called $n$ -decomposable in $G$ if it is a union of $n$ distinct $G$ -conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained...

The general methods of finding the sum $S_{n}$ for all kinds of series, II

K. Orlov (1981)

Matematički Vesnik

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The existence of $P (α)$ -points of N* for $ℵ_{0} α < 𝔠$

A. Szymański (1977)

Colloquium Mathematicae

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Asymptotic nature of higher Mahler measure

(2014)

Acta Arithmetica

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We consider Akatsuka’s zeta Mahler measure as a generating function of the higher Mahler measure $m_{k} (P)$ of a polynomial $P,$ where $m_{k} (P)$ is the integral of $l o g^{k} | P |$ over the complex unit circle. Restricting ourselves to P(x) = x - r with |r| = 1 we show some new asymptotic results regarding $m_{k} (P)$ , in particular $| m_{k} (P) | / k! \to 1 / π$ as k → ∞.

Displaying similar documents to “Less than 2 ω many translates of a compact nullset may cover the real line”

Displaying similar documents to “Less than $2^{ω}$ many translates of a compact nullset may cover the real line”