Consider the map T : [0, 1] → [0, 1], T(x) = {1/x} where {.} denotes the fractional part. Find all fixed points of T, i.e. all points r so that T(x) = x. Find countably many different Borel...

Extracted text: Consider the map T : [0, 1] → [0, 1], T(x) = {1/x} where {.} denotes the fractional part. Find all fixed points of T, i.e. all points r so that T(x) = x. Find countably many different Borel probability measures u so that ([0, 1], B, µ, T) is a p.p.t. and µ is ergodic. = T.