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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

9 votes

Sierpinski's construction of a non-measurable set

I think the pages 249-250 are the most relevant source in ariane's pdf. Sierpinski outlines how to go from the cardinality hypothesis to the existence of a non-measurable set, as per Ashutosh's précis …
Richard Chapling's user avatar
7 votes
1 answer
474 views

Under $\neg CH$, have countable unions of rationally independent numbers inner measure zero?

In their 1943 paper On non-denumerable graphs, Erdos and Kakutani suggest as likely the following proposition. (EK*) Suppose CH fails and $\lbrace M_n : n \in \omega \rbrace$ is a countable family of …