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UID:20260829T163412EDT-393860asri@132.216.98.100
DTSTAMP:20260829T203412Z
DESCRIPTION:Title: Differentiation along rectangles\n	Abstract:Lebesgue’s di
 fferentiation theorem states that\, when $f$ is a locally integrable funct
 ion in Euclidean space\, its average on the ball $B(x\,r)$ centered at $x$
  with radius $r$\, converges to $f(x)$ for almost every $x$\, when $r$ app
 roaches zero. Many questions arise when the family of balls $\{B(x\,r)\}$ 
 is replaced by a differentiation basis $\mathcal{B}=\bigcup_x \mathcal{B}_
 x$ (where\, for each $x$\, $\mathcal{B}_x$ is\, roughly speaking\, a colle
 ction of sets shrinking to the point $x$). In this case\, one looks for co
 nditions on $\mathcal{B}$ such that the average of $f$ on sets belonging t
 o $\mathcal{B}_x$ are known to converge to $f(x)$ for a.e. $x$\, when thos
 e sets shrink to the point $x$. Many interesting phenomena happen when set
 s in $\mathcal{B}$ have a rectangular shape (Lebesgue’s theorem may or may
  not hold in this case\, depending on the geometrical properties of sets i
 n $\mathcal{B}$). In this talk\, we shall discuss some of the history arou
 nd this problem\, as well as recent results obtained with E. D’Aniello and
  J. Rosenblatt in the planar case\, when the rectangles in $\mathcal{B}$ a
 re only allowed to lie along a fixed sequence of directions.\n
DTSTART:20180613T173000Z
DTEND:20180613T183000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Laurent Moonens (Paris-Sud)
URL:https://www.mcgill.ca/mathstat/channels/event/laurent-moonens-paris-sud
 -287592
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