Constructive Measure Theory (Memoirs of the American Mathematical Society, no. 116)

By Errett Bishop And Henry Cheng. Bibliography: P. 85. A general, constructive measure theory is given in terms of Daniell integrals as part of the systematic development of the constructive component of analysis. Integration spaces are first defined in terms of a linear function on the space of integrable functions on a basic set. The space of integrable functions is then extended by continuity. Integrable sets are defined, their properties proved. A theory of profiles is introduced to prove the existence of (to construct) an abundance of integrable sets. The usual convergence theorems are proved. The more common measure space approach is then dealt with and shown to be equivalent to the integration space approach taken. Product measures are constructed and Fubini's theorem proved, and the approach taken by the authors is elegant and general. Constructive proofs are immediately linked to computations