The sum of Rademacher functions and Hausdorff dimension
نویسنده
چکیده
For 0 < a < 1, let/a(x) = 2,1,2~ Ri(x) for 0 s$ x < 1, where {#,}£, is the sequence of Rademacher functions. We give a class of fa so that their graphs have Hausdorff dimension 2 —a. The result is closely related to the corresponding unsolved question for the Weierstrass functions.
منابع مشابه
On the L-pointwise Regularity of Functions in Critical Besov Spaces
We show that the functions in L(R) given by the sum of infinitely sparse wavelet expansions are regular, i.e. belong to C∞ L2(x0), for all x0 ∈ R which is outside a set of vanishing Hausdorff dimension.
متن کاملThe Hausdorff dimension of pulse-sum graphs
We consider random functions formed as sums of pulses F (t) = ∞ ∑ n=1 n −α/D G(n(t−Xn)) (t ∈ R ) where Xn are independent random vectors, 0 < α < 1, and G is an elementary “pulse” or “bump”. Typically such functions have fractal graphs and we find the Hausdorff dimension of these graphs using a novel variant on the potential theoretic method.
متن کاملHistoric set carries full hausdorff dimension
We prove that the historic set for ratio of Birkhoff average is either empty or full of Hausdorff dimension in a class of one dimensional non-uniformly hyperbolic dynamical systems.
متن کاملRademacher Complexity
Rademacher complexity is a measure of the richness of a class of real-valued functions. In this sense, it is similar to the VC dimension. In fact, we will establish a uniform deviation bound in terms of Rademacher complexity, and then use this result to prove the VC inequality. Unlike VC dimension, however, Rademacher complexity is not restricted to binary functions, and will also prove useful ...
متن کاملRademacher averages and phase transitions in Glivenko-Cantelli classes
We introduce a new parameter which may replace the fat-shattering dimension. Using this parameter we are able to provide improved complexity estimates for the agnostic learning problem with respect to any norm. Moreover, we show that if fat ( ) = ( ) then displays a clear phase transition which occurs at = 2. The phase transition appears in the sample complexity estimates, covering numbers esti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1989