Corrigendum to “On the conjecture of Ulam on the invariance of measure in the Hilbert cube” (Colloq. Math. 152 (2018), 79–95)
Volume 164 / 2021
Colloquium Mathematicum 164 (2021), 161-170
MSC: Primary 28C10; Secondary 28C20.
DOI: 10.4064/cm7145C-12-2018
Published online: 5 August 2020
Abstract
In this corrigendum, we mainly revise Lemma 5.1 of the paper by introducing an extension $F : {\rm GS}(J,p) \to M_a$ of the surjective $d_a$-isometry $f : J \to K$, where $J$ is an infinite-dimensional interval defined as $ J = \prod _{i=1}^\infty J_i $ with intervals $J_i = [ p_{1i}, p_{2i} ]$ ($0 \leq p_{1i} \lt p_{2i} \leq 1$ for $i \in \{ 1, \ldots , n \}$ and $p_{1i} = 0$, $p_{2i} = 1$ for $i \gt n$) and with the generalized linear span ${\rm GS}(J,p)$ of $J$ with respect to $p$.
