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Van Lambalgen's Theorem for uniformly relative Schnorr and computable randomness
We correct Miyabe's proof of van Lambalgen's Theorem for truth-table Schnorr randomness (which we will call uniformly relative Schnorr randomness). An immediate corollary is one direction of vanExpand
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Topics in algorithmic randomness and computable analysis
This dissertation develops connections between algorithmic randomness and computable analysis. In the first part, it is shown that computable randomness can be defined robustly on all computableExpand
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Oscillation and the mean ergodic theorem for uniformly convex Banach spaces
Abstract Let $ \mathbb{B} $ be a $p$-uniformly convex Banach space, with $p\geq 2$. Let $T$ be a linear operator on $ \mathbb{B} $, and let ${A}_{n} x$ denote the ergodic average $(1/ n){\mathop{\sumExpand
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Computable randomness and betting for computable probability spaces
  • Jason Rute
  • Mathematics, Computer Science
  • Math. Log. Q.
  • 25 March 2012
TLDR
This paper provides a general method for abstracting "bit-wise" definitions of randomness from Cantor space to arbitrary computable probability spaces. Expand
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Oscillation and the mean ergodic theorem
Let B be a uniformly convex Banach space, let T be a nonexpansive linear operator, and let A_n x denote the ergodic average (1/n) sum_{i 0, the sequence has only finitely many fluctuations greaterExpand
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ALGORITHMIC RANDOMNESS, MARTINGALES AND DIFFERENTIABILITY
In this paper, a number of almost-everywhere convergence theorems are looked at using computable analysis and algorithmic randomness. These include various martingale convergence theorems andExpand
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Energy randomness
TLDR
We show that X ∈ 2ω is s-energy random if and only if∑n∈ω2sn−KM(X↾n)<∞, providing a characterization of energy randomness via a priori complexity KM. Expand
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When does randomness come from randomness?
  • Jason Rute
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 20 August 2015
TLDR
We show that if $F\colon2^{\mathbb{N}} is an almost-everywhere computable, measure-preserving transformation, then there is a Martin-L\"of random $x\in2^{N}}$ such that $F(x)=y$. Expand
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Schnorr randomness for noncomputable measures
  • Jason Rute
  • Mathematics, Computer Science
  • Inf. Comput.
  • 15 July 2016
TLDR
This paper explores a novel definition of Schnorr randomness for noncomputable measures. Expand
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METASTABLE CONVERGENCE THEOREMS
The dominated convergence theorem implies that if (fn) is a se- quence of functions on a probability space taking values in the interval (0,1), and (fn) converges pointwise a.e., then ( R fn)Expand
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