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<pre style="text-align:center"><b style="mso-bidi-font-weight:normal"><span style="font-size:24.0pt;font-family:"Times New Roman","serif";
mso-ansi-language:EN-US" lang="EN-US">Kathryn Hare<o:p></o:p></span></b></pre>
<pre style="text-align:center"><i style="mso-bidi-font-style:normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif"">University of <span style="mso-spacerun:yes"> </span>Waterloo, Canada<o:p></o:p></span></i></pre>
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<pre style="text-align:center"><b style="mso-bidi-font-weight:normal"><span style="font-size:24.0pt;font-family:"Times New Roman","serif";
mso-ansi-language:EN-US" lang="EN-US">“Local dimensions of convolutions of measures”<o:p></o:p></span></b></pre>
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mso-ansi-language:EN-US" lang="EN-US">Abstract:<o:p></o:p></span></b></p>
<pre style="text-align:justify"><i style="mso-bidi-font-style:normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif";
mso-ansi-language:EN-US" lang="EN-US">A measure on R that is concentrated on a set of Lebesgue measure zero is called singular. For such measures it is of interest to quantify their degree of singularity, and one way to do this is to compute their local dimensions.
For many interesting classes of singular measures, including self-similar measures and Cantor-like measures that satisfy a suitable separation condition, it has long been known that the set of attainable values for the local dimensions is a closed interval.
More recently, it was discovered that this is not true for the 3-fold convolution of the classical Cantor measure.
In fact, we will see that under modest assumptions, convolutions of continuous, singular measures always have an isolated point in their set of local dimensions. <o:p></o:p></span></i></pre>
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<pre class="moz-signature" cols="72">--
--------------------------------------------------------------------------------
Valeria Giuliani
Scuola Normale Superiore
Servizio alla Didattica e Allievi
Tel. 050-509260
Piazza dei Cavalieri, 7
56126 Pisa
E-Mail: <a class="moz-txt-link-abbreviated" href="mailto:v.giuliani@sns.it">v.giuliani@sns.it</a>
E-Mail: <a class="moz-txt-link-abbreviated" href="mailto:classi@sns.it">classi@sns.it</a>
Le informazioni contenute nella presente e-mail e nei relativi allegati possono essere riservate e sono, comunque, destinate esclusivamente al destinatario in indirizzo.
E’ vietata, pertanto, la diffusione, distribuzione e/o copiatura di tali informazioni da parte di qualsiasi soggetto diverso dal destinatario.
Chiunque abbia ricevuto o letto questa e-mail per errore o senza esserne legittimato č invitato a darne immediatamente notizia al mittente tramite fax o e-mail e a distruggerla.
Grazie.
</pre>
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