מִתְאַבְּלִין עַל פִּי עֵד אֶחָד, וְעֵד מִפִּי עֵד, וּבְנָכְרִי מֵסִיחַ לְפִי תֻמוֹ. 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.1Any testimony that is sufficient to permit one’s wife to remarry is certainly sufficient for the laws of mourning. Ramban.
מִי שֶׁקִּבֵּל אִגֶּרֶת שֶׁמֵּת קְרוֹבוֹ וְאֵין מְבֹאָר בָּהּ אִם הוּא עֲדַיִן תּוֹךְ שְׁלֹשִׁים אוֹ לְאַחַר שְׁלֹשִׁים, אִם הַכּוֹתֵב אֵינוֹ בַעל תּוֹרָה, מוֹקְמֵינָן לָאָדָם בְחֶזְקַת חַי, וְאָמְרִינָן שֶׁלֹּא מֵת עַד סָמוּךְ לִכְתִיבַת הָאִגֶּרֶת, וְחַיָב לְהִתְאַבֵּל. אֲבָל אִם הַכּוֹתֵב הוּא בַעַל תּוֹרָה, אָמְרִינָן מִסְּתָמָא הוּא לְאַחַר שְׁלֹשִׁים. דְּאִם אִיתָא שֶׁהָיָה אֶפְשָׁר שֶׁתַּגִּיעַ הָאִגֶּרֶת לְיָדוֹ תּוֹךְ שְׁלֹשִׁים, לֹא הָיָה כוֹתֵב בִּסְתָם. אַךְ אִם הוּא אָבִיו אוֹ אִמּוֹ, כֵּיוָן שֶהַמִּנְהָג הוּא לְהוֹדִיעַ מִיָד (לְעֵיל סוֹף סִימָן רו), חַיָּב לְהִתְאַבֵּל. 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.2Bach, Shach. If however, he was informed of the death of his father or his mother, since it is customary to notify [the son] immediately,3So that he can say Kaddish. he must observe the laws of mourning.4Sh’vuss Yaakov vol. 1 Responsa 98.