Can the average of a function be defined as the sum of its image over its cardinality?

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In practice, when calculating the average, this is essentially what you are doing. You are summing up an infinite number of function values (the functions image), and dividing by that infinite number (the cardinality of the set that contains the functions image). So is this statement correct? I haven't seen it stated this way anywhere, so I am unsure if it is correct.