Abstract
Recall that the curvature measures C k(X r, ⋅) of the r-parallel sets to a set X with positive reach converge vaguely to those of X itself (see Corollary 4.35). This stability result motivates a natural question whether curvature measures of more general sets can be introduced through approximation with parallel sets. This will indeed be the case, as it will be clear in Chap. 9. However, not only parallel sets may be used for approximation. Classically, approximations by polyhedral (piecewise linear) sets are frequently used in differential geometry, or approximation by smooth sets in different ways.
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Rataj, J., Zähle, M. (2019). Approximation of Curvatures. In: Curvature Measures of Singular Sets. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-18183-3_7
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DOI: https://doi.org/10.1007/978-3-030-18183-3_7
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