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A recent comprehensive presentation of Steffensen's inequality is provided in [8, Chapter XI].In the present paper, we extend Steffensen's inequality from integrals over compact intervals of the real line to integrals over general measure spaces. We apply this generalization to establish integral inequalities for composed functions. Then we obtain stronger particular inequalities by means of the concept of Wrightconvexity. The key tools that we use here are the concepts of separating subsets for a measurable function, and continuous measure spaces. We establish convexity properties of integrals over separating subsets of a continuous measure space, which provide interpolations of our inequalities, and also new expressions for the monotone rearrangement of a function.

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