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We start from the following problem: given a function $f : [0, 1] \to [0, 1]$ what can be said about the set of points in the range where level sets are «big» according to an opportune definition. This yields the necessity of an analysis of the structure of level sets of $C^{n}$ functions. We investigate the analogous problem for $C^{n, a}$ functions. These are in a certain way intermediate between $C^{n}$ and $C^{n + 1}$ functions. The results involve a mixture of Real Analysis, Geometric Measure Theory and Classical Descriptive Set Theory.

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Increasing functions.

Infinitely Differentiable Functions With Prescribed Derivatives At A Point.

Integration by Parts

Invariance of the Cauchy mean-value expression with an application to the problem of representation of Cauchy means.

Investigation of smooth functions and analytic sets using fractal dimensions

Currently displaying 1 – 5 of 5