So, the basic idea is that any pair consisting of a 'set' and its 'sigma-algebra' is considered a "measurable space" and any triplet consisting of a 'set', its 'sigma-algebra', and a 'probability measure' is a probability space. (*with their associated properties...)
So, "in words" -- a sigma-algebra tells you more or less HOW to measure intervals on the 'space' defined by the 'set' using some subset of its elements (the basis set?) that contains the null, and the probability measure tells you HOW to define the probability of a particular interval on this measurable space? so, then is there a relationship between the associated sigma-algebra, the probability space and notions of 'continuous' vs 'discrete' distributions? . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
