Is it permissible to implement legal punishments (Hudud) in the frontier regions (Thughur)?

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Implementing the legal punishments (Hudud) in the frontier regions is permissible without any known disagreement. This is because these regions are considered part of the lands of Islam, and there is a necessity to deter their inhabitants, similar to the necessity for deterring others. Umar wrote to Abu Ubaidah commanding him to flog anyone who consumed alcohol eighty times while he was in Sham, which is one of the frontier regions.