31. Saying 10 unit intervals ( or 10 UI ), actually means 10 times the definite predetermined time called " UI ". 32. The Hilbert cube is homeomorphic to the product of countably infinitely many copies of the unit interval [ 0, 1 ]. 33. *The classical Wiener space " C " 0 of unit interval [ 0, 1 ] has another integration by parts operator. 34. Wiener's original construction only applied to the space of real-valued continuous paths on the unit interval , known as classical Wiener space. 35. For example, an idealized vibrating string can be modelled as the graph of a function on the unit interval , with fixed ends. 36. Formally, the circle is the quotient space of the unit interval obtained by setting the endpoints of the interval to be equivalent. 37. :You have attempted to conquer the problem that the edges may have indefinite length by definining a transformation to the unit interval . 38. Another generalization was given by Kleiber and Pervin ( 1969 ) : a metric space of product of copies of the unit interval . 39. For any set X, a membership function on X is any function from X to the real unit interval [ 0, 1 ]. 40. The \ sup and \ inf respectively take the supremum and infimum over pdf's on the unit interval ( actually Borel probability measures ).
