Support theorems for the Radon transform and Cramér-Wold theorems
نویسندگان
چکیده
This article presents extensions of the Cramér-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distribution theory and Fourier analysis we show that the presented injectivity results for the Radon transform lead to Cramér-Wold type results for measures. One purpose of this article is to contribute to making known to probabilists interesting results for the Radon transform that have been developed essentially during the 1980ies and 1990ies.
منابع مشابه
On a Conjecture Concerning a Theorem of Cramér and Wold
Both theorems, (I) and the stronger (II), although they are very simple in their statements, have been conjectured to require Fourier analysis for their proofs; see, e.g., p. 396 of Billingsley [2] for the first and p. 49 of Billingsley [1] for the second part. This note gives probabilistic proofs of the two theorems and thus answers this conjecture to the negative. The main argument of the pro...
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