In the past I have listed the things that build a continuity of experience but I have not given a Formal (read Dictionary) definition. So here it goes:
conÂ·tiÂ·nuÂ·iÂ·ty of exÂ·peÂ·riÂ·ence
a coherent whole understanding of an object, thought, or emotion through the senses or mind.
Via American Heritage dictionary