How Long to Read On Sudakov’s Type Decomposition of Transference Plans with Norm Costs

How Long Does it Take to Read On Sudakov’s Type Decomposition of Transference Plans with Norm Costs?

It takes the average reader 1 hour and 52 minutes to read On Sudakov’s Type Decomposition of Transference Plans with Norm Costs by Stefano Bianchini

Assuming a reading speed of 250 words per minute. Learn more

Description

The authors consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost with , probability measures in and absolutely continuous w.r.t. . The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in , where are disjoint regions such that the construction of an optimal map is simpler than in the original problem, and then to obtain by piecing together the maps . When the norm is strictly convex, the sets are a family of -dimensional segments determined by the Kantorovich potential called optimal rays, while the existence of the map is straightforward provided one can show that the disintegration of (and thus of ) on such segments is absolutely continuous w.r.t. the -dimensional Hausdorff measure. When the norm is not strictly convex, the main problems in this kind of approach are two: first, to identify a suitable family of regions on which the transport problem decomposes into simpler ones, and then to prove the existence of optimal maps. In this paper the authors show how these difficulties can be overcome, and that the original idea of Sudakov can be successfully implemented. The results yield a complete characterization of the Kantorovich optimal transportation problem, whose straightforward corollary is the solution of the Monge problem in each set and then in . The strategy is sufficiently powerful to be applied to other optimal transportation problems.

How long is On Sudakov’s Type Decomposition of Transference Plans with Norm Costs?

On Sudakov’s Type Decomposition of Transference Plans with Norm Costs by Stefano Bianchini is 112 pages long, and a total of 28,224 words.

This makes it 38% the length of the average book. It also has 34% more words than the average book.

How Long Does it Take to Read On Sudakov’s Type Decomposition of Transference Plans with Norm Costs Aloud?

The average oral reading speed is 183 words per minute. This means it takes 2 hours and 34 minutes to read On Sudakov’s Type Decomposition of Transference Plans with Norm Costs aloud.

What Reading Level is On Sudakov’s Type Decomposition of Transference Plans with Norm Costs?

On Sudakov’s Type Decomposition of Transference Plans with Norm Costs is suitable for students ages 10 and up.

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