Regular variation in 𝑅^{𝑘}

Meerschaert, Mark M.

doi:10.1090/S0002-9939-1988-0920997-5

Regular variation in $\textbf {R}^k$
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by Mark M. Meerschaert

Proc. Amer. Math. Soc. 102 (1988), 341-348

DOI: https://doi.org/10.1090/S0002-9939-1988-0920997-5

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Abstract:

Researchers investigating certain limit theorems in probability have discovered a multivariable analogue to Karamata’s theory of regularly varying functions. The method uses elements of real analysis and Lie groups to analyze the asymptotic behavior of functions and measures on ${{\mathbf {R}}^k}$. We present an account here which is independent of probabilistic considerations.

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Regular variation in

and the Abel-Tauber Theorem