Sale on Boundaries: 1+1

During the 60,s and the 70,s Furstenberg developed two parallel theories regarding boundaries of groups of different flavours. One is topological, and the other is measurable and relates to random walks. The research of these two theories and their connections with rigidity theory and operator algebra theory is still very active, yet many questions are open. In an attempt to understand better the connections between them, I’ll show that they share the same driving force. We סwill develop one machinery to produce them both at the same time. Two Boundary Theories for the price of one.