Three approaches to functional integration are compared: Feynman's definiti
on and the Feynman-Kac formula, Bryce DeWitt's formalism, and the authors'
axiomatic scheme. They serve to highlight the evolution of functional integ
ration in the second half of the twentieth century. (C) 2000 American Insti
tute of Physics. [S0022-2488(00)00306-6].