dr lee peng yee and rydolf vyborny book describes gauges in the plane as a rectangle containing each point.
a delta fine tagged net partition may not exist . As discussed in Mcleod. we need to consider bipartitions
But consider a gauge d1 in first component an interval d2 in second component again an interval.
so we can form product gsuge d by cartesian product of these two gauges. a net partition exists. for such gauges.
the only result which ails if the indicator function of a set Z has integral 0 then any function which is 0 except on Z is integrable with integral 0.
this is not needed in fubini as when one iterated integral does not exist the set is considered as null set only in one component.
so using product gauges may simplify fubini.
convergence theorems will hold ?
will some expert may be Dr lee peng yee or Dr Vyborny clarify
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