Alexander Pruss
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 Sep 26 awarded Yearling Mar 23 comment How many subsets of $[0,1)$ are there modulo null sets? @Asaf: It's a bit strange to me, too. I would have expected countable or dependent choice would be all that's needed to prove that there are $c$ Borel sets (and thanks for the catch that $c^2=c$). Maybe we should just try to write out one of the standard proofs very carefully. (No time right now for me.) Mar 20 revised Finitely additive measures on $\mathbb Z_2^\omega$ with invariance and independence constraints added 10 characters in body Mar 20 answered Consequences of ZF+“all subsets of reals are Lebesgue measurable” Mar 20 comment How many subsets of $[0,1)$ are there modulo null sets? Actually it seems to. The Consequences of AC page says that 8 (Countable Choice) is true and 363 ($2^c$ Borel sets) is false in $\cal M5(\aleph)$ and $\cal M38$. Mar 20 comment How many subsets of $[0,1)$ are there modulo null sets? Does it use anything beyond countable choice? Mar 20 accepted How many subsets of $[0,1)$ are there modulo null sets? Mar 20 comment How many subsets of $[0,1)$ are there modulo null sets? Agreed, though there are questions about what values for the cardinality are options without AC. (E.g., if all sets are measurable then we get $\le c^2$, assuming that the proof that there are $c$ Borel sets goes through without AC.) Mar 20 comment How many subsets of $[0,1)$ are there modulo null sets? Thanks! The existence of a set $S$ with the requisite properties (well, or the equivalent claim on the square) also follows from Sierpinski's 1938 partition of the square into perfect sets such that any choice of one element of each of the perfect sets gives a set with full outer measure: eudml.org/doc/213031 Mar 19 awarded Nice Question Mar 19 asked How many subsets of $[0,1)$ are there modulo null sets? Sep 26 awarded Yearling Sep 24 awarded Autobiographer Jul 21 revised Embedding probability spaces in the completion of $[0,1]^K$ cleanup Jul 17 revised Embedding probability spaces in the completion of $[0,1]^K$ need completion for lifting Jul 17 revised Embedding probability spaces in the completion of $[0,1]^K$ added 52 characters in body Jul 16 revised Embedding probability spaces in the completion of $[0,1]^K$ replace "finite measure" with "probability" for clarity Jul 16 asked Embedding probability spaces in the completion of $[0,1]^K$ Jul 8 answered Products of Boolean algebras and probability measures thereon Jul 2 awarded Curious