graph of that function and the X axis. The Lebesgue integral, named after French mathematician Henri Lebesgue, is one way to make this concept rigorous...

aire ("Integral, length, area") at the University of Nancy during 1902. Henri Lebesgue was born on 28 June 1875 in Beauvais, Oise. Lebesgue's father was...

early 20th century, Henri Lebesgue generalized Riemann's formulation by introducing what is now referred to as the Lebesgue integral; it is more general than...

{\displaystyle f:[a,b]\to \mathbb {R} } , the product integral reduces exactly to the case of Lebesgue integration, that is, to classical calculus. Thus,...

theorem is named for Henri Lebesgue. For a Lebesgue integrable real or complex-valued function f on Rn, the indefinite integral is a set function which maps...

integrals (Integraltafeln) and techniques of integral calculus was published by the German mathematician Meier Hirsch [de] (also spelled Meyer Hirsch) in 1810...

its introduction of the Lebesgue integral. It was in 1912, "the only textbook on analysis containing both Lebesgue integral and its application to Fourier...

Pettis integral or Gelfand–Pettis integral, named after Israel M. Gelfand and Billy James Pettis, extends the definition of the Lebesgue integral to vector-valued...

monotonically grow. It is also called the Cantor ternary function, the Lebesgue function, Lebesgue's singular function, the Cantor–Vitali function, the Devil's staircase...

passing to a limit. In practice, the integral is often regarded as an improper integral instead of a proper Lebesgue integral, but sometimes for convergence...