Margulis–Russo formula

For the indicator $f$ of a monotone family under a p-biased product measure, the Margulis–Russo formula identifies the derivative of ${\mathbb{E}}_{{\mu }_p}f$ with the suitably normalized total influence of $f$.

A coordinate is pivotal for an increasing event in a configuration when changing only that coordinate changes whether the event occurs. Its pivotal probability is the coordinate's influence.