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Crazy Sets of Rectangles and (Non)Convergence Theorems in Analysis

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When you write the Fourier series of your favorite function, does the series actually converge to your function? If you average a function f on smaller and smaller balls centered at a point x, does these averages converge to f(x)? How about if we average over rectangles instead? If a collection of rectangles has the area of their union being bounded, and we double the length of each rectangle, what is the area of the new union? Can it be unbounded? My talk will be about the connections between these questions.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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