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Aggregation of data values plays an important role on distributed computations, in particular over peer-to-peer and sensor networks, as it can provide a summary of some global system property and direct the actions of self-adaptive distributed algorithms. Examples include using estimates of the network size to dimension distributed hash tables or estimates of the average system load to direct load-balancing. Distributed aggregation using non-idempotent functions, like sums, is not trivial as it is not easy to prevent a given value from being accounted for multiple times; this is especially the case if no centralized algorithms or global identifiers can be used. This paper introduces Extrema Propagation, a probabilistic technique for distributed estimation of the sum of positive real numbers. The technique relies on the exchange of duplicate insensitive messages and can be applied in flood and/or epidemic settings, where multi-path routing occurs; it is tolerant of message loss; it is fast, as the number of message exchange steps equals the diameter; and it is fully distributed, with no single point of failure and the result produced at every node.