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Limiting distributions examples of an invariance
More general formulations of the invariance
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algorithms assumption belonging to L2 Brownian motion process Cameron and Martin Chapter characteristic function coefficients condition construction continuous function converges corresponding denote differential space differential-space theory distribution function Doob dX(t eigenvalues Einstein ensemble Equation ergodic ergodic hypothesis example expression formula Fortet function X(t functions defined Gaussian given hidden variables Hilbert space hypothesis increments independent inequality integral invariance principle Lebesgue measure lemma Math mathematical mean zero measurable functions measure space measure theory metrically transitive nonnegative notation obtained orthogonal particle physical observables positive integer postulate prediction probability functional space probability space probability theory projection operator proof properties quantum mechanics quantum systems quasi-intervals random variables relation result sample functions satisfying Section sequence set of functions set of points spectral statistical mechanics statistically independent step function stochastic process subsets tion transformation unit circle unit interval values vector wave function zero and variance