R. J. Adler, The Geometry of Random Field, 1981.
DOI : 10.1137/1.9780898718980

R. J. Adler, On excursion sets, tube formulas and maxima of random fields, The Annals of Applied Probability, vol.10, issue.1, pp.1-74, 2000.
DOI : 10.1214/aoap/1019737664

R. J. Adler, G. Samorodnitsky, and J. E. Taylor, Excursion sets of three classes of stable random fields, Advances in Applied Probability, vol.9, issue.02, pp.293-318, 2010.
DOI : 10.1214/aoap/1177005437

R. J. Adler, G. Samorodnitsky, and J. E. Taylor, High level excursion set geometry for non-Gaussian infinitely divisible random fields. The Annals of Probability, pp.134-169, 2013.

R. J. Adler, E. Subag, and J. E. Taylor, Rotation and scale space random fields and the Gaussian kinematic formula, The Annals of Statistics, vol.40, issue.6, pp.2910-2942, 2012.
DOI : 10.1214/12-AOS1055

R. J. Adler and J. E. Taylor, Random fields and geometry, 2007.
DOI : 10.1137/1.9780898718980

L. Ambrosio, N. Fusco, and D. Pallara, Free Discontinuity Problems and Special Functions with Bounded Variation, 2000.
DOI : 10.1007/978-3-0348-8974-2_2

F. Baccelli and B. Bb-laszczyszyn, Stochastic Geometry and Wireless Networks, Volume I ? Theory?4 of Foundations and Trends in Networking, 2009.

Y. Baryshnikov and R. Ghrist, Euler integration over definable functions, Proc. Natl. Acad. Sci. USA, pp.9525-9530, 2010.
DOI : 10.1007/s00222-008-0114-1

H. Biermé and A. Desolneux, Crossings of smooth shot noise processes, The Annals of Applied Probability, vol.22, issue.6, pp.2240-2281, 2012.
DOI : 10.1214/11-AAP807

H. Biermé and A. Desolneux, On the perimeter of excursion sets of shot noise random fields. The Annals of Probability, pp.521-543, 2016.

M. Bilodeau and D. Brenner, Theory of multivariate statistics. Springer Texts in Statistics, 1999.

O. Bobrowski and M. S. Borman, EULER INTEGRATION OF GAUSSIAN RANDOM FIELDS AND PERSISTENT HOMOLOGY, Journal of Topology and Analysis, vol.10, issue.01, pp.49-70, 2012.
DOI : 10.1007/BFb0082775

L. Decreusefond, E. Ferraz, H. Randriambololona, and A. Vergne, Simplicial Homology of Random Configurations, Advances in Applied Probability, vol.2011, issue.02, pp.325-347, 2014.
DOI : 10.1214/09-AOP477
URL : https://hal.archives-ouvertes.fr/hal-00578955

E. , D. Bernardino, A. Estrade, and J. R. León, A test of Gaussianity based on the Euler Characteristic of excursion sets, Electron. J. Stat, vol.11, issue.1, pp.843-890, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01345225

A. Estrade and J. R. León, A central limit theorem for the Euler characteristic of a Gaussian excursion set. The Annals of Probability, pp.3849-3878, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00943054

L. C. Evans and R. F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, 1992.

L. Heinrich and V. Schmidt, Normal convergence of multidimensional shot noise and rates of this convergence, Advances in Applied Probability, vol.18, issue.04, pp.709-730, 1985.
DOI : 10.2307/3212048

M. Hirsch, Differential Topology, 1976.
DOI : 10.1007/978-1-4684-9449-5

R. Lachì-eze-rey, Bicovariograms and Euler characteristic I. Regular sets, 2015.

R. Lachì-eze-rey, Bicovariograms and Euler characteristic II Random fields excursions https://arxiv.org/abs/1510.00502. [23] R.Lachì eze-Rey. Two-dimensional Kac-Rice formula. Application to shot noise processes excursions, 2015.

R. D. Macpherson, Chern Classes for Singular Algebraic Varieties, The Annals of Mathematics, vol.100, issue.2, pp.423-432, 1974.
DOI : 10.2307/1971080

K. R. Mecke, Exact moments of curvature measures in the Boolean model, Journal of Statistical Physics, vol.102, issue.5/6, pp.1343-1381, 2001.
DOI : 10.1023/A:1004800714563

K. R. Mecke and H. Wagner, Euler characteristic and related measures for random geometric sets, Journal of Statistical Physics, vol.19, issue.3-4, pp.843-850, 1991.
DOI : 10.1007/BF01048319

J. W. Milnor, On the Total Curvature of Knots, The Annals of Mathematics, vol.52, issue.2, pp.248-257, 1950.
DOI : 10.2307/1969467

I. Molchanov, Theory of Random Sets. Probability and its applications, 2005.

L. A. Santaló, Integral Geometry and Geometric Probability, 2004.

P. Schapira, Operations on constructible functions, Journal of Pure and Applied Algebra, vol.72, issue.1, pp.83-93, 1991.
DOI : 10.1016/0022-4049(91)90131-K

R. Schneider and W. Weil, Stochastic and integral geometry. Probability and its Applications, 2008.
DOI : 10.1007/978-3-540-78859-1

D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic geometry and its applications Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, 1987.

C. Thäle, 50 years sets with positive reach?a survey, Surv. Math. Appl, vol.3, pp.123-165, 2008.

O. Y. Viro, Some integral calculus based on Euler characteristic, Topology and geometry?Rohlin Seminar, pp.127-138, 1988.
DOI : 10.1307/mmj/1029001529

K. J. Worsley, Local Maxima and the Expected Euler Characteristic of Excursion Sets of Chi2, F and t Fields, Advances in Applied Probability, vol.26, issue.3, pp.13-42, 1994.

K. J. Worsley, The Geometry of Random Images, CHANCE, vol.12, issue.1, pp.27-40, 1996.
DOI : 10.1038/jcbfm.1992.127