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We characterize the Carleson measures for an exponential Bergman space on theunit ball of $\mathbb C^n$ in terms of the ball induced by the complex Hessianof the logarithm of the weight function. The boundedness (or compactness) ofintegral operators, Ces\`{a}ro operators and Toeplitz operators, is given usingthe Carleson measure (or vanishing Carleson measure) characterization.

Carleson embedding theorem for an exponential Bergman space on the unit ball