Posted private establishments can prevent permit holders from carrying a firearm within their business. "Posting" or notification can be done with a sign that meets the requirements of MN 624.714 subd. 17 or be done verbally (see statute below). Failure to comply with postings may result in legal action and law enforcement interaction. The general rule is that if you wish to shop at a business that is "posted" leave your firearm secured in your car. Otherwise, spend your money elsewhere. If you ignore the signs and refuse to leave when asked to do so, you will most likely be charged with trespass. Follow the law and there will be no issue (generally speaking).