Tomasz Żuchowski: Nonseparable growth of omega supporting a strictly positive measure
14/03/16 18:57
Tuesday, March 15, 2016 17:15
Room: D1-215
Speaker: Tomasz Żuchowski
Title: Nonseparable growth of omega supporting a strictly positive measure
Abstract. We will construct in ZFC a compactification \(\gamma\omega\) of \(\omega\) such that its remainder \(\gamma\omega\backslash\omega\) is not separable and carries a strictly positive measure, i.e. measure positive on nonempty open subsets. Moreover, the measure on our space is defined by the asymptotic density of subsets of \(\omega\).
Our remainder is a Stone space of a Boolean subalgebra of Lebesgue measurable subsets of \(2^{\omega}\) containing all clopen sets.
Room: D1-215
Speaker: Tomasz Żuchowski
Title: Nonseparable growth of omega supporting a strictly positive measure
Abstract. We will construct in ZFC a compactification \(\gamma\omega\) of \(\omega\) such that its remainder \(\gamma\omega\backslash\omega\) is not separable and carries a strictly positive measure, i.e. measure positive on nonempty open subsets. Moreover, the measure on our space is defined by the asymptotic density of subsets of \(\omega\).
Our remainder is a Stone space of a Boolean subalgebra of Lebesgue measurable subsets of \(2^{\omega}\) containing all clopen sets.