Henri Lebesgue (nonfiction)

Henri Léon Lebesgue.

Henri Léon Lebesgue ForMemRS (French: [ɑ̃ʁi leɔ̃ ləbɛɡ]; June 28, 1875 – July 26, 1941) was a French mathematician most famous for his theory of integration, which was a generalization of the 17th century concept of integration—summing the area between an axis and the curve of a function defined for that axis. His theory was published originally in his dissertation Intégrale, longueur, aire ("Integral, length, area") at the University of Nancy during 1902.

Lebesgue invented a new method of integration (finding the area under the graph of a function). Lebesgue looked at the codomain of the function for his fundamental unit of area. Lebesgue's idea was to first define measure, for both sets and functions on those sets. He then proceeded to build the integral for what he called simple functions; measurable functions that take only finitely many values. Then he defined it for more complicated functions as the least upper bound of all the integrals of simple functions smaller than the function in question.

As part of the development of Lebesgue integration, Lebesgue invented the concept of measure, which extends the idea of length from intervals to a very large class of sets, called measurable sets (so, more precisely, simple functions are functions that take a finite number of values, and each value is taken on a measurable set). Lebesgue's technique for turning a measure into an integral generalises easily to many other situations, leading to the modern field of measure theory.

Lebesgue wrote, "Réduites à des théories générales, les mathématiques seraient une belle forme sans contenu." ("Reduced to general theories, mathematics would be a beautiful form without content.")

Nonfiction cross-reference

• Mathematician (nonfiction)

External links:

• Henri Lebesgue @ Wikipedia