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Results tagged with reference-request
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user 61785
This tag is used if a reference is needed in a paper or textbook on a specific result.
9
votes
A characterization of $L_1(\mu)$ in $L_\infty(\mu)^*$
The criterion suggested in the question works fine for $\sigma$-finite spaces, and Michael Greinecker's answer is correct under this assumption.
However, the suggested criterion is not (provably) suf …
- 3,768
3
votes
Is the space of Radon measures a Polish space or at least separable?
The other answers very adequately explain why the norm topology is not Polish except for trivial cases, so this answer is about the weak-* topology. Also, most results in the literature are about the …
- 3,768
3
votes
Reference: If $X$ is metrizable, then $X$ is realcompact iff $|X|$ is non-measurable
Here is some information on the history of the result, which was actually proven before Shirota's 1952 theorem. It was proved in 1948 by Marczewski and Sikorski as Theorem VI in:
Marczewski, E.; Sikor …
- 3,768
2
votes
Properties of measures that are not countably additive but have countably additive null ideals
$\newcommand{\N}{\mathbb{N}}\newcommand{\R}{\mathbb{R}}$There are examples on $\R$ with the Borel $\sigma$-algebra $\mathcal{B}$. We take the null ideal to be the meagre Borel sets $\mathcal{M}$ (the …
- 3,768
1
vote
Accepted
Is a Boolean algebra with an order continuous topology a measure algebra?
It is not true that $B$ is necessarily a measure algebra. The counterexample is due to Michel Talagrand, who constructed a Maharam algebra that is not a measure algebra.
Maharam, D., An algebraic cha …
- 3,768