Geodesic
Dirac Delta Functions Via Nonstandard Analysis
Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 759-762

Voir la notice de l'article provenant de la source Cambridge University Press

We recall that a Dirac delta function δ(x) in the real number system is the idealization of a function that vanishes outside a "short" interval and satisfies It is conceived as a function δ for which δ(0)=+ ∞, δ(t)=0 if t≠0, and This function should possess the "sifting property" for any continuous function f. Even though certain sequences of functions are used, via a limit operation, to approximate a Dirac delta function (for details, see [3] and [4]), no function in has these properties. 
Lightstone, A. H.; Wong, Kam. Dirac Delta Functions Via Nonstandard Analysis. Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 759-762. doi: 10.4153/CMB-1975-132-3
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[1] 1. Robinson, A., Non-standard Analysis, North-Holland Amsterdam 1966. Google Scholar

[2] 2. Kelemen, P.J. and Robinson, A., The Non-standard : Model 1. The Technique of Nonstandard Analysis in Theoretical Physics, J. Math. Phys., Vol. 13, No. 12, Dec. 1972. Google Scholar

[3] 3. Erdélyi, A., Operation Calculus and GeneralizedFunctions, Holt, Rinehart and Winston, Inc., 1962. Google Scholar

[4] 4. Pol, Balth. van der and Bremmer, H., Operational Calculus; Cambridge University Press, 1955. Google Scholar

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