Summary: For nonnegative \(L\)-measurable functions \(u:\mathbb{R}^n\to\mathbb{R}\) a continuous homotopy \(u^t\), \(0\leq t\leq+\infty\), is constructed, connecting \(u\) with its Steiner-symmetrization \(u^*\). It is shown that a number of familiar relations between \(u\) and \(u^*\) including some integral inequalities are also valid for \(u\) and \(u^t\). The method is applicable to prove symmetry properties of stationary solutions of variational problems.