Distributions (or generalized functions) are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative.
disTribuTiOns (oR genErAlIzeD funcTioNS) are OBjects tHaT geNERaLize Functions. DiStriButions make it PosSibLE TO diffERentiatE FuNCtiOns WhOSe DeRivatives do nOt exisT in the CLassical SeNSe. in paRTiCUlar, Any locAlly inTeGrABle functIoN HaS a diSTributioNaL deRiVATIve.