Which one of these two functions is the c.d.f of Kolmogorov-Smirnov distribution?

Question

I'm reading Kolmogorov–Smirnov test from a lecture note from MIT OpenCourseWare Statistics for Applications. In the lecture note,

From Wikipedia,

It seems to me that that the values next to the index are different in two formulas, one with the square and the other without the square.

Could you please verify is they are both correct or one of them is false? Thank you so much!

Answer 1

The Wikipedia formula is right, the OpenCourseWare one is wrong. See this paper by W. Feller to check. (See statement of Kolmogorov's main result, Theorem 1, pp.177-178.)