Problem of the Nile

[1] It is presented by Dubins and Spanier in the following words:[2]"Each year, the Nile would flood, thereby irrigating or perhaps devastating parts of the agricultural land of a predynastic Egyptian village.

The value of different portions of the land would depend upon the height of the flood.

William Feller showed in 1938 that a solution for the general case might not exist.

[3] When the number of different heights (= measures) is finite, a solution always exists.

This was first noted by Jerzy Neyman in 1946, and proved as a corollary of the Dubins–Spanier theorems in 1961.