==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: ‘Decompress current Excalidraw file’. For more info check in plugin settings under ‘Saving’

Excalidraw Data

Text Elements

Embedded Files

59e63e8496c406e3453d869acfd6737dae654818: \(x\)

919e60cf1f77dd03a167b10419662e019b622980: \(y\)

88416097adefb6662bd1390b228bfbfc80b8418a: \(z\)

a5ff35080114ea060ab4906d43f0ad57f2c23422: \(\nu (x, y)\)

fb8bf57de2ad366d04467b572edf57a3d8721930: \(\nu (y, z)\)

1e41875f238d504d4f2adf0f6eb12bf13fb42e82: \(\nu (x, z)\)

66e1c7cbd85ee3737b1253ebd4d556260ab23355: \(\textcolor{green}{\nu (x, z)} \leq \textcolor{blue}{\nu (x, y) + \nu (y, z)}\)

4ec2ba3190c03b7cecfba3c4872866034fded499: \(x\)

d444101a9e83efd4dca39cf5fe62565f97701c1a: \(y\)

6c6040a8fcb5b0601c991efbe42bbd1887a54f96: \(z\)

fc6244951e15bc979f1512d958bec3e99082a2fb: \(\nu (x, y)\)

1dc049cb6f97a0dfee1ab8d1dcde12c936d43721: \(\nu (x, z)\)

2e395006bbfa18cb66329fb8ffe9f94bac020b87: \(\textcolor{orange}{\nu (x, y)} \geq \textcolor{green}{\nu (x, z)} \textcolor{red}{- \nu (y, z)}\)

6592a3e48b4bb0552f1c7cf4b90c551a2fbbb09f: \(\nu (y, z)\)

4a080f05a754c0452fcf27dc6573e104c9672922: \(x\)

93a09eb7595702d04830e67a0c777c895b2f7974: \(y\)

ab5cc1163ba0c58bc654ef29d90fa27c5c82cc52: \(z'\)

fbcd2c157a77aadaa2137884ec3dde218dfee5d4: \(\nu (x, y)\)

34786dc091e2f046c6726cc158fd5f81946857ff: \(\textcolor{orange}{\nu (x, y)} = \sup_{z' \in \mathcal X} \bigg( \textcolor{green}{\nu (x, z')} \textcolor{red}{- \nu (y, z')} \bigg)_+\)

498c26bb0645695948dd7a9f55d9958d9a1df23c: \(x\)

8f5ddd0733c49b0fd8c0b93ef5de15898460cfd0: \(x\)

5d12728db575aab8656e931d44fa51725620db15: \(y\)

713ae05d0d2dd95069eab6d02bd59484b36eaf2a: \(y\)

631970f6358b5cae05419925614d8670dc887ce3: \(z'\)

0666e8f87c8321dae1ea1e61b6c79cdccd9a13d3: \(z'\)

9e74762c684fca824ec9d387c2b9375999fc52e2: \(\nu (x, y)\)

dfe9c10922dacde9c44725aa469133063ea3a78a: \(\nu (x, y)\)

ec8735746c98b24aef310a4ecdf344bda2933874: \(f(z) = f(z; x, y) = \bigg( \textcolor{green}{\nu (x, z)} \textcolor{red}{- \nu (y, z)} \bigg)_+\)

ebdc5a4b1a2f7d2fac34fde85afa397c806f27ac: \(\mathcal X\)

a1b45d0f38bd7e912b115bfd4c4180dc255b1c34: \(\xi_1\)

42d3e77741ecb99e9ca5802358c87b46825671fc: \(\xi_j\)

db0a70e0975cde4edbb4044f42c55520f2e89447: \(\xi_K\)

671fab88403eeeea5cbc0ffd9312a81f471247ae: \(\xi_i\)

7c27a50dcb7b991549f7d0f7f581cb08e5424d35: \(\xi_2\)

07b6b37c847d033045d4a6ae7c3e51f96e662b76: \(\xi_k\)

bef1428dbd412432047f5705223f8dd2d2d502f9: \(\delta\)

167f02013a4eda26fc7b391ac5e17a47de0df53b: \(\mathcal X\)

ac0153df38253c373970b26c208fc688dd923705: \(x\)

774fee7958115501febbdac9de9e5444cbf88530: \(\xi_k\)

fd3e7ae8bd14b07d06594c79119f50f337b995ea: \(\xi_K\)

2bad1336839cfcc3132cd529f9d0b0552f64f2ea: \(\xi_j\)

605ee058c022989737ef4bf114e23ce432a9760b: \(\xi_1\)

78de8302842f6cc2ed759224b8cd9d76a8f1e7e3: \(\xi_2\)

bc5016f1fbf64fe82e34bfc68918c4b0f779378e: \(\xi_i\)

ac22c70c99d14e948646bb5d78f2c0d67bf1fe1b: \(y\)

3baca510f2f8d3778392e23c448ed83097e5b14b: $$\begin{aligned} d (x, y) &= \max_{\xi_i} \bigg[

& \textcolor{blue}{\big(\nu (x, \xi_1) - \nu (y, x_1) \big)+},
& & \textcolor{red}{\big(\nu (x, \xi_2) - \nu (y, x_2) \big)
+},
& & \dots
& & \textcolor{green}{\big(\nu (x, \xi_K) - \nu (y, x_K) \big)_+}

\bigg] \

\end{aligned}$$

%%

Drawing

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