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Furstenberg boundary

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In mathematics, specifically harmonic analysis and probability theory, the Furstenberg boundary is a notion of boundary associated with a group. It is named for Harry Furstenberg, who introduced it in a series of papers beginning in 1963 (in the case of semisimple Lie groups). The Furstenberg boundary can be characterized as a universal boundary space for harmonic analysis on the group, in the sense that bounded harmonic functions can be represented by their boundary values via a Poisson-type integral.