I wish to write code for Riemann-Stieltjes integrals in Mathematica.
A necessary condition for the theorem to hold is that the function must be continuous. The domain of the function is a closed real interval containing infinitely many points, so I can't check continuity at each and every point.
I wish to know if there are any built-in functions in Mathematica that determine if a function is continuous or not. Or if there is any function that returns point of singularities of function?
D[g[x, y], x, y, x]
returns `Derivative[2, 1][g][x, y], even though these are not in general the same (though they are in the presence of certain smoothness requirements). mathematica.stackexchange.com/questions/32872/… is related. $\endgroup$