Timeline for Does pointwise convergence yield the convergence under Skorokhod topology?

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Jun 30, 2022 at 7:11	comment	added	user478657		Many thanks for the answer. Indeed I meant this counterexample for the case where $f_n$ is non-decreasing (with a mistake in my statement), but obviously your example is still adapted
Jun 30, 2022 at 7:09	vote	accept	CommunityBot
Jun 29, 2022 at 21:36	comment	added	Iosif Pinelis		@Philo18 : No, there is no typo here: $1(t<1)$ is right-continuous in $t$.
Jun 29, 2022 at 20:36	history	edited	Iosif Pinelis	CC BY-SA 4.0	added 38 characters in body
Jun 29, 2022 at 20:29	history	edited	Iosif Pinelis	CC BY-SA 4.0	added 38 characters in body
Jun 29, 2022 at 20:20	comment	added	user478492		It seems to me that there is one more typo. The limit is denoted by $\hat f(t):=1_{\{t<1\}}$. As for $f$, it is the right-continuous modification of $\hat f$, which means $f(t):=1_{\{t\le 1\}}$
Jun 29, 2022 at 20:15	comment	added	Iosif Pinelis		@Philo18 : yes; this is now corrected. Thank you for your comment.
Jun 29, 2022 at 20:13	history	edited	Iosif Pinelis	CC BY-SA 4.0	edited body
Jun 29, 2022 at 20:12	comment	added	user478492		Is the limit given as $f(t):=1_{\{t<1\}}$?
Jun 29, 2022 at 20:01	history	edited	Iosif Pinelis	CC BY-SA 4.0	added 131 characters in body
Jun 29, 2022 at 19:55	history	answered	Iosif Pinelis	CC BY-SA 4.0