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Results tagged with measure-theory
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user 100163
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
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Concentration-compactness for Radon measures on a metric space
It is known (see Ch. 4 in Struwe's Variational Methods) that Radon measures on $\mathbb{R}^n$ satisfy the concentration-compactness principle. Does the same hold true for Radon measures on a general m …
- 660
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Reference request: sequential weak* topology on the space of signed Radon measures
Consider the space $\mathcal{M}_{loc} (\mathbb{R}^d)$ of locally finite signed Radon measures, equipped with the weak* topology in duality with $C_b (\mathbb{R}^d)$. It is known that this is space is …
- 660
1
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Loeb measures and non-standard hull of Banach spaces
Yes, $f:\Omega \rightarrow \hat{V}$ has a lifting to some function $F : \Omega \rightarrow V$. This is shown in section 4 of the paper "Lifting theorems in nonstandard measure theory", D. Ross, 1990: …
- 660
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Reference request: "doubly empirical" measure associated to a random measure
I am considering the following type of situation. Suppose we have a random probability measure, by which I mean a probability measure on a space of probability measures atop some Polish space $X$. In …
- 660
2
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Uniformization/measurable selection theorems
Bogachev's Measure Theory, Vol. 2 Chapter 6, section 9 is a survey of measurable selection theorems written in the 2000s. It mentions a handful of results which were published in the 80s, but nothing …
- 660
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Are the sublevel sets of Boltzmann entropy compact in Wasserstein distance?
It is known that the sublevel sets of the relative entropy are tight when the reference measure is finite, and in fact are also compact in the topology of setwise convergence (which is stronger than t …
- 660