About the Daniel integral

In the 10s of the 20th century, integration penetrates into spaces that are increasingly moving away from their prototype-the n - dimensional Euclidean space. The need to go beyond Euclidean spaces was dictated mainly by the development of functional analysis. When considering in spaces of General nature, it has become inconvenient to associate the integration of a function with the properties of elements and subsets of the space itself (among these properties, the most important is the existence of a class of sets of a certain algebraic nature with a given measure on it). In some questions, the point of view of the integral as a function of the set has become inconvenient, and it is inferior to the point of view of the integral as a functional. An expression of this new trend is the definition of Daniel, given by him in 1919.