Definition of Tight Measure given in this article is not the same as Inner Regular Measure. For example, the article says that if we take ${\displaystyle X=[0,\omega _{1}]}$ with its order topology there is a measure ${\displaystyle \mu }$ that is not tight. But this cannot be so, since ${\displaystyle K_{\varepsilon }=X}$ is such that ${\displaystyle \mu (X\setminus K_{\varepsilon })=\mu (\emptyset )=0<\varepsilon }$ for any ${\displaystyle \varepsilon >0}$.

André Caldas (talk) 00:48, 26 February 2015 (UTC)Reply[reply]

Mathematics C‑class Low‑priority

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The section about Polish spaces says: "If ${\displaystyle X}$ is a compact Polish space, then every probability measure on ${\displaystyle X}$ is tight." This is stupid. If ${\displaystyle X}$ is compact, then all sets of probability measures are tight, not just the singletons (see a couple lines above) and Prokhorov's theorem is toothless.

The correct assertion is "If ${\displaystyle X}$ is a compact Polish space, then every probability measure on ${\displaystyle X}$ is tight." This arise from the separability of Polish spaces, btw. For instance see Lemma 3.2 in http://www.math.chalmers.se/~serik/C-space.pdf

69.204.248.106 (talk) 20:57, 8 March 2021 (UTC)Reply[reply]

Hi, what you say makes sense but:

1. Striking out text in articles is not the way to make correction. This does not help anyone.

2. Your "correct assertion" is a verbatim copy of the statement you are criticizing, and the document you linked is not accessible. So it is not clear what you are trying to say.

Best, Malparti (talk) 11:24, 14 October 2021 (UTC)Reply[reply]