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math105-s22:s:mchlxo:start [2022/05/06 08:24]
mchlxo [Proposition 1]
math105-s22:s:mchlxo:start [2026/02/21 14:41] (current)
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 $$ E(\phi) = \int_{\mathcal{P}} \phi(\omega) d \mu(\omega)$$ $$ E(\phi) = \int_{\mathcal{P}} \phi(\omega) d \mu(\omega)$$
 for each $\phi(\omega)$ with a continuous $F$ on $\mathcal{P}$ for each $\phi(\omega)$ with a continuous $F$ on $\mathcal{P}$
 +
 +==== References ====
 +Sternberg, Shlomo Z. 2014. “Wiener Measure.” Harvard Math 201a, November 11.\\
 +\\
 +Taylor, Michael E. 2006. Measure Theory and Integration. Graduate Studies in Mathematics, v. 76. Providence, R.I: American Mathematical Society.\\
 +\\
 +Wright, David G. 1994. “Tychonoff’s Theorem.” Proceedings of the American Mathematical Society 120 (3): 985–87. https://doi.org/10.1090/S0002-9939-1994-1170549-2.
 +
 +
 ===== Resources ===== ===== Resources =====
 A {{ :math105-s22:s:mchlxo:exception_points.pdf |paper}} that constructs a set which includes points at which the density of the set can take on any values in $[0,1]$ A {{ :math105-s22:s:mchlxo:exception_points.pdf |paper}} that constructs a set which includes points at which the density of the set can take on any values in $[0,1]$
  
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