Henri Léon Lebesgue was a French mathematician known for his contributions to the field of measure theory. He developed the Lebesgue integral, which extends the concept of integration beyond the traditional Riemann integral. This new approach allows for the integration of a broader class of functions, making it essential in modern analysis. Lebesgue's work laid the foundation for various areas in mathematics, including probability theory and functional analysis. His ideas have influenced many other fields, enabling mathematicians to tackle complex problems involving limits, continuity, and convergence in a more rigorous way.