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Browsing by Author Le, Xuan Son

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  • Article

  • The extreme value of local dimension of convolution of the cantor measure

    • Authors: Vu, Thi Hong Thanh; Nguyen, Quang Quynh; Le, Xuan Son (2009)

  • Let $\mu$ be the $m-$fold convolution of the standard Cantor measure and $\underline{\alpha}_m$ be the lower extreme value of the local dimension of the measure $\mu$. The values of $\underline{\alpha}_m$ for $m=2,3,4$ were showed in [4] and [5]. In this paper, we show that $$\underline{\alpha}_5=|\frac{\log \big[\frac{2}{3.2^5}\big(\sqrt{145}\cos(\frac{\arccos\frac{427}{59\sqrt{145}}}{3})+5\big)\big]}{\log 3}|\approx 0.972638.$$ This values was estimated by P. Shmerkin in [5], but it has not been proved.
  • 138.pdf.jpg
  • Article

  • On weak convergence in the space of probability capcacities in Rd*

    • Authors: Nguyen, Nhuy; Le, Xuan Son (2003)

  • In this paper we are going to extend the weak convergence in the space probality measures to the one in the space of probality capacities and investigate the relation in weak convergence between probality capacities and their associated probality measures.

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Browsing by Author Le, Xuan Son

Jump to: 0-9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
or enter first few letters:  
Showing results 1 to 5 of 5
  • 112.pdf.jpg
  • Article

  • The extreme value of local dimension of convolution of the cantor measure

    • Authors: Vu, Thi Hong Thanh; Nguyen, Quang Quynh; Le, Xuan Son (2009)

  • Let $\mu$ be the $m-$fold convolution of the standard Cantor measure and $\underline{\alpha}_m$ be the lower extreme value of the local dimension of the measure $\mu$. The values of $\underline{\alpha}_m$ for $m=2,3,4$ were showed in [4] and [5]. In this paper, we show that $$\underline{\alpha}_5=|\frac{\log \big[\frac{2}{3.2^5}\big(\sqrt{145}\cos(\frac{\arccos\frac{427}{59\sqrt{145}}}{3})+5\big)\big]}{\log 3}|\approx 0.972638.$$ This values was estimated by P. Shmerkin in [5], but it has not been proved.
  • 138.pdf.jpg
  • Article

  • On weak convergence in the space of probability capcacities in Rd*

    • Authors: Nguyen, Nhuy; Le, Xuan Son (2003)

  • In this paper we are going to extend the weak convergence in the space probality measures to the one in the space of probality capacities and investigate the relation in weak convergence between probality capacities and their associated probality measures.