29 The Ham-Sandwich Theorem

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This is episode 29 of a course on algebraic topology.

We give a rare example of a real-world application of algebraic topology. Due to lack of ham we use a cheese sandwich.

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7:02-7:30 That moment, when your proof is not constructive and you just have to leave your sandwich on the desk...

georgfrenck
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21:58 For dominated convergence you need the dominating function to be integrable: The constant function 1 would be dominating the sequence of characteristic functions of the intervals [n, n+1], which converges pointwise to the characteristic function of the empty set.

Great video, nonetheless!

georgfrenck
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If I suppose take A_1 as a line passing through the origin in a two-dimensional Euclidean plane(E) and A_2 some circle, now lebsuge measure of A_1 is zero which is finite and it also a borel subset in E with respect to the lebsuge measure in E. In that case I think this theorem may be not true, ....may be I am wrong.

totanghosh
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Does this also hold for vegan sandwiches?

poisoniveej