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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- …

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 …

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 …

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 …

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 …

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 …

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 …