Many of these ideas can be seen or at least hinted at in the movie Memento. One such idea is that of psychological continuity theory, which states that your identity is based on certain psychological characteristics that exist continuously from the moment of a person's birth. In this theory these characteristics can include memories, morals, values, conscience and personality. Interestingly, using these criteria, I don't think we can say that Leonard is the same person throughout the entire film. Since Leonard does not have the ability to create new memories and does not maintain the same morals, values, or personality that he had before the accident, it is difficult to use the theory of psychological continuity to justify that Leonard is the same person as before. The next theory that addresses this issue is the theory of physical continuity, which states that a person's identity is based on a body that has existed continuously from the moment of birth until now. I think using this theory one can make a strong case that Leonard is still the same person. Since Leonard has continuously possessed the same body since the moment of his birth, he can be said, using the theory of physical continuity, to be the same person he was before his death.