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0 $begingroup$ I would like to justify the following claim concerning thin sets found in Chung, Lectures from Markov Processes to Brownian Motion , page 112: Such a set is finely separated in the sense that each of its points has a fine neighborhood containing no other point of the set. The context is the general theory of Hunt processes. The state space, which is assumed metrizable and compact, is denoted $mathcal{E}_{partial}$ . A (non-necessarily Borel) set $A$ is said to be finely open is for each $x in A$ , there is a Borel set $B subset A$ such that $P^{x}[T_{B^c} > 0] = 1$ where $T_{E} equiv inf{ t > 0,;, X_t in E }$ denotes the hitting time of a (nearly-)Borel set $E$ for the Hunt process $(X_t)_{t geq 0}$ and $P^x$ is the probability measure with initial distribution concentrated on...

0 $begingroup$ Consider the generic p-series: $sum_{n=1}^{infty}frac{1}{n^{p}}$ Let the increment function be: $n= n+K$ where $K$ is some integer constant. For $K=1$ its simple p-series and that diverges for any $p<1$ . Can we have some integer value of $K$ beyond which the series converges for $p<1$ . Specifically for $ 1/2 < p <1.$ real-analysis share | cite | improve this question asked Dec 18 '18 at 10:27 TheoryQuest1 TheoryQuest1 141 7 $endgroup$ ...