Algorithmic definitions of singular functions

A function f on an interval [a; b] is singular if f(a) < f(b), f is increasing (non-
decreasing), f is continuous everywhere and f0(x) = 0 almost everywhere. In this
thesis, we focus on the strictly increasing singular functions of DeRham and Minkowski.
We propose algorithmic definitions of each of these functions, and use these new defini-
tions to provide alternative proofs of known properties about the values and derivatives
of these functions. Before that, we give some background on sets of discontinuity for
general functions, for increasing functions, and some background on the derivatives of
increasing functions.
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Abstract/Description: A function f on an interval [a; b] is singular if f(a) < f(b), f is increasing (non- decreasing), f is continuous everywhere and f0(x) = 0 almost everywhere. In this thesis, we focus on the strictly increasing singular functions of DeRham and Minkowski. We propose algorithmic definitions of each of these functions, and use these new defini- tions to provide alternative proofs of known properties about the values and derivatives of these functions. Before that, we give some background on sets of discontinuity for general functions, for increasing functions, and some background on the derivatives of increasing functions.
Subject(s): Monotonic functions. -- Mathematics -- Singular Functions