The same set of Bourgain points and the convergence of approximated identities and Bourgain points of bounded functions is described. A class of kernels, such that any bounded function is strongly approximated by the convolutions at each of its points, is also described. The mean variation of the function over an interval is defined by including one more averaging in the definition of a vertical interval. Strong convergence at the B-points of bounded functions is also observed for approximate identities with a different structure. It is shown that for any kernal, there exists a real-valued function and the vertical variation of the interval is infinite almost everywhere. For a compactly supported kernel of a certain class, there exists a real-valued function for which the vertical interval is infinite everywhere.