"Burden of establishing" a fact means the burden of persuading the trier of fact that the existence of the fact is more probable than its nonexistence.

对某项事实承担“举证责任”，指承担说服该事实之审判人，使其相信该事实存在之可能性大于其不存在之可能性的责任。

youdao

Adjudicative facts mean the judgments or presumptions made by the trier of fact about the objective facts concerning the case, on the basis of the evidences, through the procedure.

裁判事实是事实审理者通过法定程序，在证据的基础上，对案件涉及的客观事实所作的一种认定或推定。

youdao

If nothing else, it is probable enough that the issue should be decided by a trier of fact, not on a motion to dismiss.

在不考虑其他问题的情况下，这个可能性已经够大，因而应该用事实进行审判，而不是通过驳回案件的动议来决定这个问题。

youdao

This requires the government to carry the heavy burden of persuading the trier of fact that beyond a reasonable doubt that the elements of the crime are proved.

FORBES: Nothing Civil About Asset Forfeiture

"I think that the testimony will cause the trier of fact to question some of the central and primary themes the prosecution has offered, " said Simpson attorney Carl Douglas.

CNN: Prosecution rests rebuttal case in Simpson trial

To prevail in a civil case, the plaintiff need only persuade the trier of fact by a mere preponderance of evidence that the elements of the cause of action have been proved.

FORBES: Nothing Civil About Asset Forfeiture