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Results tagged with reference-request
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user 100163
This tag is used if a reference is needed in a paper or textbook on a specific result.
6
votes
1
answer
230
views
Reference request: acceleration/curvature of curve in metric space
Let $(X,d)$ be a metric space. Given a continuous curve $\gamma_t : [0,1] \rightarrow X$, the metric speed is defined by $$ |\gamma_t^\prime | := \lim_{s\rightarrow t} \frac{d(\gamma_s, \gamma_t)}{|t- …
- 660
1
vote
0
answers
54
views
Lax CD(K, $\infty)$ space in the sense of Sturm
In K.T. Sturm's "On the geometry of metric measure spaces. I", Definition 4.5, he introduces a "lax" version of the usual CD(K,$\infty$) lower bound. Namely, one allows for $\epsilon$-approximate leng …
- 660
0
votes
0
answers
54
views
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
votes
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
16
votes
3
answers
1k
views
What are some interesting examples of non-classical dynamical systems? (Group action other t...
By classical dynamical system, I mean a measure space together with a measurable action of the integers or the reals. Of course, this action is often interpreted as evolution with respect to discrete …
0
votes
Properties of the topology of sequential convergence $\tau_\text{seq}$
I am aware of two general topology textbooks which discuss sequential spaces: (probably there is also discussion in earlier works by e.g. Frechet, Kuratowski...)
General Topology I by Arkhangel'skii …
- 660
1
vote
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