 The significance of common cause complete spaces is that they display a very strong compliance with the Common Cause Principle: An equivalent formulation of the Common Cause Principle is that probability theories describing the world are causally closed in the following sense: if A and B are correlated and are causally independent, \(R_{ind}(A,B)\) in notation, then the correlation has to have a common cause that explains the correlation. Common cause complete spaces are causally closed in the extremely strong sense that the causal independence relation \(R_{ind}(A,B)\) can be taken to be the strongest one, containing all correlated events. Thus, if a scientific theory describing some aspect of reality uses a measure theoretically purely non-atomic probability space, such a theory can be regarded as evidence in favor of the Common Cause Principle because that theory contains common causes of all correlations, including correlations that are between events that the theory might regard as causally unrelated (independent). In view of the interpretation of common cause completeness, common cause completability and common cause extendability, it is a relevant question whether our well-confirmed scientific theories are causally closed or common cause extendable. Quantum field theory and standard non-relativistic quantum mechanics are two theories for which this questions has been analyzed extensively.