  This work proves pointwise convergence of the truncated Fourier double
integral of non-Lebesgue integrable bounded variation functions. This leads to
the Dirichlet-Jordan theorem proof for non-Lebesgue integrable functions, which
has not been sufficiently studied. Note that recent contributions regarding
this subject consider Lebesgue integrable functions, [F. Moricz, 2015], [B.
Ghodadra-V. Fuulop, 2016].
