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Questions tagged [real-analysis]

Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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How do we introduce a signed finite measure on the space of curves confined into the box $[0,1]^{n}$?

Given $\Omega_{n} = \{\alpha:[0,1]\rightarrow[0,1]^{n}\,|\,\alpha\,\,\text{is smooth}\}$, consider the equivalence relation: \begin{align*} & \alpha_{1} \sim \alpha_{2} \Leftrightarrow \int_{0}^{1}...