In a criminal case, all the elements of the crime must be proved by the government beyond a reasonable doubt.

Reasonable doubt which will justify acquittal is doubt based on reason and arising from evidence or lack of evidence, and it is doubt which a reasonable man or woman might entertain, and it is not fanciful doubt, is not imagined doubt, and is not doubt that a juror might conjure up to avoid performing an unpleasant task or duty.  Reasonable doubt is such a doubt as would cause prudent people to hesitate before acting in matters of importance to themselves.

Source:  Black's Law Dictionary (5th edition).