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High Quality Content by WIKIPEDIA articles! In mathematics, the secondary measure associated with a measure of positive density when there is one, is a measure of positive density , turning the secondary polynomials associated with the orthogonal polynomials for into an orthogonal system.Under certain assumptions that we will specify further, it is possible to obtain the existence of a secondary measure and even to express it. These secondary measures, and the theory around them, lead to some surprising results, and make it possible to find in an elegant way quite a few traditional formulas of analysis, mainly around the Euler Gamma function, Riemann Zeta function, and Euler's constant. They also allowed the clarification of integrals and series with a tremendous effectiveness, though it is a priori difficult.