The test of the sufficiency of the notice is merely whether it includes information sufficient to enable the city to investigate. In making this determination, the Court may look at, among other things, the evidence adduced at the section 50-h hearing.
Here, according to the notice and evidence adduced at the 50-h hearing, plaintiff states that while she was on an escalator inside the train station, she slipped and fell on a slippery condition. Plaintiff alleges that the escalator was within the control of the agency and that it failed to maintain the escalator. Accordingly, the agency was on notice of plaintiff's theory of liability, namely, that it has a duty to use reasonable care to maintain the escalator in a safe condition.
Ingrao v. New York City Tr. Auth., NY Slip Op 03889 (1st Dep't May 31, 2018)
Here is the decision.