"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。

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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