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Mar 9, 2017 at 18:05 vote accept Eduardo
Mar 7, 2017 at 6:43 comment added Julian Newman This is a very nicely formulated question: although it initially appears as though some of your assumptions should be redundant, I have had to use every single one for my proof below (except the continuity of $h_n$, and the added statement about the measures having compact support).
Mar 7, 2017 at 6:40 answer added Julian Newman timeline score: 3
Mar 6, 2017 at 23:38 history edited Eduardo CC BY-SA 3.0
added 64 characters in body
Mar 6, 2017 at 20:44 comment added Eduardo @Nate Eldredge the convergence is locally compact
S Mar 6, 2017 at 20:11 history suggested J.J. Green CC BY-SA 3.0
minor typographic fixes
Mar 6, 2017 at 20:05 review Suggested edits
S Mar 6, 2017 at 20:11
Mar 6, 2017 at 19:35 comment added Christian Remling This will work as soon as you can guarantee that $h_n\, d\nu_n$ is close to $h\, d\nu_n$, and this will be the case under mild additional assumptions (for example, $\| h_n -h\|_{L^1(d\nu_n)}\to 0$ would give you that these measures are in fact close in norm).
Mar 6, 2017 at 19:27 comment added Nate Eldredge In what sense does $h_n \to h$? Pointwise convergence is not enough.
Mar 6, 2017 at 19:24 history edited Nate Eldredge CC BY-SA 3.0
spelling and grammar corrections
Mar 6, 2017 at 19:17 history asked Eduardo CC BY-SA 3.0