Kitzur Shulchan Aruch - Chapter 218: The Law of Testimony Relating to Mourning

A person must observe the laws of mourning on the testimony of one witness, or the testimony of a witness who heard about is from another witness, or by the disinterested statement of a non-Jew.1

How should one who receives a letter notifying him of the death of his relative conduct himself when it is not clear whether it is still within thirty days of the death, or after thirty days. If the writer is not learned in Torah, we assume that the relative was alive, and did not die until right before the letter was written, and thus he must observe mourning for him. However, if the writer is learned in Torah, we assume it is after the thirty days, for if it were possible that the letter would arrive during the first thirty days, he would not have written it without specifiying the date.2 If however, he was informed of the death of his father or his mother, since it is customary to notify [the son] immediately,3 he must observe the laws of mourning.4