We consider integrals in the sense of Choquet with respect to the \(\delta \) -dimensional Hausdorff content for continuously differentiable functions defined on open, connected sets in the Euclidean n-space, \(n\ge 2\) , \(0<\delta \le n\) . In particular, for these functions we prove Sobolev inequalities in the limiting case \(p=\delta /n\) and in the case \(p>\delta \) , here p is the integrability exponent of the absolute value of the gradient of any given function. The results complement previously known Poincaré–Sobolev and Morrey inequalities.
