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In this paper we look at the topological type of algebraic sum of achievement sets. We show that there is a Cantorval such that the algebraic sum of its $k$ copies is still a Cantorval for any $k \in \mathbb{N}$. We also prove that for any $m,p \in (
Externí odkaz:
http://arxiv.org/abs/2309.01589
Autor:
Glab, Szymon, Marchwicki, Jacek
The main result is that the celebrated Guthrie-Nymann's Cantorval has comeager set of uniqueness. On the other hand many other Cantorvals have meager set of uniqueness.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/2203.12479
Autor:
Głab, Szymon, Marchwicki, Jacek
Let $\mu$ be a purely atomic measure. By $f_\mu:[0,\infty)\to\{0,1,2,\dots,\omega,\mathfrak{c}\}$ we denote its cardinal function $f_{\mu}(t)=\vert\{A\subset\mathbb N:\mu(A)=t\}\vert$. We study the problem for which sets $R\subset\{0,1,2,\dots,\omega
Externí odkaz:
http://arxiv.org/abs/1911.01206
Autor:
Szymon Glab, Jacek Marchwicki
Publikováno v:
Results in Mathematics. 78
The main result is that the celebrated Guthrie-Nymann's Cantorval has comeager set of uniqueness. On the other hand many other Cantorvals have meager set of uniqueness.
14 pages
14 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::56b77ea1e2d5d0075f70e22b7f24195c
https://doi.org/10.1007/s00025-022-01777-3
https://doi.org/10.1007/s00025-022-01777-3
Autor:
Szymon Gła̧b, Jacek Marchwicki
Let $$\mu $$ μ be a purely atomic finite measure. Without loss of generality we may assume that $$\mu $$ μ is defined on $${\mathbb {N}}$$ N , and the atoms with smaller indexes have larger masses, that is $$\mu (\{k\})\ge \mu (\{k+1\})$$ μ ( { k
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a9e5ad0132552d23efe637ac3ac96628
http://arxiv.org/abs/1911.01206
http://arxiv.org/abs/1911.01206