This work arises from lecture notes for a two semester basic course sequence in Measure and Probability Theory given for first year Statistics graduate students at the University of North Carolina, evolving through many generations of handwritten, typed, mimeographed, and finally LaTeX editions. Their focus is to provide basic course material, tailored to the background of our students, and influenced very much by their reactions and the changing emphases of the years. We see this as one side of an avowed department educational mission to provide solid and diverse basic course training common to all our students, who will later specialize in diverse areas from the very theoretical to the very applied.

The notes originated in the 1960's from a “Halmos style” measure theory course. As may be apparent (to those of sufficient age) the measure theory section has preserved that basic flavor with numerous obvious modernizations (beginning with the early use of the Sierpinski-type classes more suited than monotone class theorems for probabilistic applications), and exposition more tailored to the particular audience. Even the early “Halmos framework” of rings and σ-rings has been retained up to a point since these notions are useful in applications (e.g. point process theory) and their inclusion requires no significant further effort. Integration itself is discussed within the customary σ-field framework so the students have no difficulty in relating to other works.