  We first present an abstract principle for the interchange of infimization
and integration over spaces of mappings taking values in topological spaces.
New conditions on the underlying space and the integrand are then introduced to
convert this principle into concrete scenarios that are shown to capture those
of various existing interchange rules. These results are leveraged to improve
state-of-the-art interchange rules for evaluating Legendre conjugates,
subdifferentials, recessions, Moreau envelopes, and proximity operators of
integral functions by bringing the corresponding operations under the integral
sign.
