The trouble is that you can split a big event into P / epsilon chance-of-epsilon events, or average P / epsilon chance-of-epsilon events into a big event. In order to avoid inconsistency, you have to actually say what information you think should be treated as an average of nearby information.
The trouble is that you can split a big event into P / epsilon chance-of-epsilon events, or average P / epsilon chance-of-epsilon events into a big event. In order to avoid inconsistency, you have to actually say what information you think should be treated as an average of nearby information.