A new class of functions, the BP (Borel-programmable) functions, is defined. It is strictly larger than the class of Borel functions, but has some similar properties, including closure under composition. All BP functions are absolutely measurable. The class of BP sets (those with BP indicators) is a Borel field and is closed under operation A. The relation of BP sets to the R-sets of Kolmogorov is not treated.
"Borel-Programmable Functions." Ann. Probab. 6 (2) 321 - 324, April, 1978. https://doi.org/10.1214/aop/1176995576