Asser Rig was a Danish tribal chief of Zealand in today's Denmark.
His wife was Inger Eriksdotter (evidently the daughter of , and Princess Cecilia Knutsdatter), with whom he had three children: Absalon, future Archbishop of Lund, Esbern Snare, and Ingefred Assersdatter.
Inger and Asser resided at Fjenneslevlille and let build Fjenneslev Kirke.