TD 2 : Gaussian processes and Brownian motion
Only care about whether d(a,b) < d(x,y), and not about the actual values. Now continuity does worry about how close d(a,b) is to d(x,y).
Section 1.6?Continuity - TDChristian Splash! PageThe continuity of functions f : R ? R considered as some applications from (R,Td) to (R,Te), where Te denotes the natural topology in R, is said approximate ... rigorous proof of hydrodynamics for symmetric simple exclusion ...Let T be an ergodic automorphism of Td as defined in the introduction. Let f be a continuous function from Td to R with modulus of continuity ?(f, ·). The ... Continuity! - dimacsClearly F0 is a pointwise limit of continuous functions, since we have F0(x) = limn?? Fn(x), where functions Fn(x) := f(x+1/n)?f(x). 1/n are clearly continuous.
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