A Recent and Modern Approach to The Moment Problem on R

The moment problem is an important problem in Functional Analysis and in Probability measure.
It goes back to Stieltjes, around 1890. There is still an important ongoing interest in the recent
literature. But, up today, the main theoretical resource (Shohat and Tamarkin, 1934) does not
have the modern exposure it deserves, especially in the current development of measure theory of
integration. Besides, the multivariate version is far less exploited. In this paper, a full exposure of
such a theory is presented, using the latest knowledge of measure theory and functional analysis. As
a result, the basis of future development is layed out and the accessibility of the theory by modern
graduate students and researchers is guaranteed.