The objective of this article is to study the boundary value problem for the general semilinear elliptic equation of second order involving L1 functions or Radon measures with finite total variation. The study investigates the existence and uniqueness of ‘very weak’ solutions to the boundary value problem for a given L1 function. However, a ‘very weak’ solution need not exist when an L1 function is replaced with a measure due to which the corresponding reduced limits has been found for which the problem admits a solution in a ‘very weak’ sense