Suppose I take the PDF of the LogNormal distribution with parameters m and s evaluated at x. I obviously get an expression involving m. I now want to integrate that expression not with respect to x but with respect to m as m goes from -infinity to infinity I get a ConditionalExpression that says the result is 1/x but on condition that x be less than 1. And, yet, if I NIntegrate the same expression when I make x greater than 1, I seem to always get the same result: 1/x. Why is Mathematica imposing what seems to be a needless condition on the result of the Integration? Why does it not know what the answer is when x>1?

 pdfv=Refine[PDF[LogNormalDistribution[m,s],x],x>0]
 Integrate[pdfv,{m,DirectedInfinity[-1],DirectedInfinity[1]}]
 With[{v1 = PDF[LogNormalDistribution[m, 0.1], 2.5]}, 
   NIntegrate[v1, {m, -\[Infinity], \[Infinity]}]] (* yields 0.4 *)
 With[{v2 = PDF[LogNormalDistribution[m, 0.1], 4.0]}, 
   NIntegrate[v2, {m, -\[Infinity], \[Infinity]}]] (* yields 0.25 *)

For what it's worth, I'm trying to get the distribution of lognormal distributions from which a single result might have occurred if we know the underlying process was lognormal. ( We also have some prior belief as to the second parameter of the underlying lognormal.)