Believe It Or Not Meaning

(idiomatic) You may not believe the following, but it is true.

Example: 2001 Bryan A. Garner, Legal writing in plain English: a text with exercises, p. 108:
  That depends on how long the sentence is. Believe it or not, there’s a canon of construction about provisos, and the test is anything but clear: …
2003 Robert Bruce Thompson and Barbara Fritchman Thompson, PC hardware in a nutshell, p. 230:
  One common cause of “flipped bit” memory errors is, believe it or not, cosmic rays.
2007 David Brown, Tchaikovsky: The Man and His Music, p. 165:
  The descending opening phrase of the aria is, believe it or not, Tatyana’s Fate theme from her Letter Scene, though now in a minor, not major key: …