In probability theory the expectation value of a random variable or observable is to be thought of as the mean value of that variable/observable under the given probabilities. Taking the concept of expectation value as the primary concept (Whittle 92) develops the theory of probability from axioms on the expectation functional rather than on the axioms of a probability measure. For a measure space of finite total measure and for an measurable function on , a random variable, then its expectation value is In terms of the probability measure this is simply the integral For classical probability (not quantum), spaces equipped with a notion of expectation value can be modeled as algebras over a probability monad. See probability monad - algebras for more.