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README.md
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@@ -723,7 +723,7 @@ Transformer architecture (Vaswani et al.) does poorly in theory of mind. What c
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> Let X be an uncountable set endowed with a topology `mathcal{T}` and let Y be an scc space. Let `phi: X -> Y` be a categorically Lebesgue measurable function, and let `|*|:
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> Y^N -> [0,+infinity]` be a "categorical modulus of continuity" in the sense that for any `x in X` and any open neighborhood `U` of `phi(x)`, there exists `M_U > 0` such that `|{y
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> in U | |phi(y_n) - phi(y_{n-1})| > M_U}|\ < epsilon` for some `N = N_U,M_U > omega` and all `epsilon > 0`. Then we define the "categorical Lebesgue integral" of phi over X
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> as:
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> `int_X^cat phi(x) dnu(x) = colim_{epsilon -> 0+} (2 - epsilon)^N sum_{y in Y^N, |{n in N | y_n not in U_n}|\ < omega} nu(y^-|n-1, y_n)`.
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> ### 5 Applications to Computability
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> Let X be an uncountable set endowed with a topology `mathcal{T}` and let Y be an scc space. Let `phi: X -> Y` be a categorically Lebesgue measurable function, and let `|*|:
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| 724 |
> Y^N -> [0,+infinity]` be a "categorical modulus of continuity" in the sense that for any `x in X` and any open neighborhood `U` of `phi(x)`, there exists `M_U > 0` such that `|{y
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> in U | |phi(y_n) - phi(y_{n-1})| > M_U}|\ < epsilon` for some `N = N_U,M_U > omega` and all `epsilon > 0`. Then we define the "categorical Lebesgue integral" of phi over X
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> as:
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>
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> `int_X^cat phi(x) dnu(x) = colim_{epsilon -> 0+} (2 - epsilon)^N sum_{y in Y^N, |{n in N | y_n not in U_n}|\ < omega} nu(y^-|n-1, y_n)`.
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> ### 5 Applications to Computability
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