English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In 1950 Maharam asked whether every disintegration of a $\sigma$-finitemeasure into $\sigma$-finite measures is necessarily uniformly $\sigma$-finite.Over the years under special conditions on the disintegration, the answer wasshown to be yes. However, we show here that the answer may depend on the axiomsof set theory in the following sense. If CH, the continuum hypothesis holds,then the answer is no. One proof of this leads to some interesting problems ininfinitary combinatorics. If G\"odel's axiom of constructibility$\mathbf{V}=\mathbf{L}$ holds, then not only is the answer no, but, of equalinterest is the construction of $\mathbf{\Pi}^1_1$ sets with very specialproperties.

CH, V=L, Disintegrations of Measures, and {\Pi}^1_1 Sets