The paper introduces the concept of a conditionally dispersed endowment distribution (given the consumption set) in the study of regularizing effect of aggregation and existence of equilibria in an exchange economy with an atomless measure space of consumers. It is shown that there is a regularizing effect of aggregation whenever the endowment distribution of an economy is conditionally dispersed. On the basis of this regularizing effect, the existence of a competitive equilibrium is proved in a very general setting where some of the commodities are indivisible and where different consumers may have different consumption sets.