Simplicial complexes; definition of simplicial homology. Basic properties. Functoriality.
Geometric realizations; simplicial approximations.
Additivity; Euler characteristic as measure. Integrals with respect to Euler characteristics.
Properties: linearity, Fubini theorem.
Classes of admissible sets.
Applications in sensor fusion.
Euler integral calculus.
Radon transform; Schapira’s inversion formula.
Describe convolution of the indicator functions of an ellipse and a circle (consider different relations between the radius of the circles and the curvatures of the ellipse).