In Discontinuous Analysis: Discontinuous and Non-Smooth Analysis, author Victor Lvovich Porton introduces the concept of generalized limits, a groundbreaking approach that challenges the boundaries of mathematical analysis.

This book explores how generalized limits extend the traditional definition of limits to encompass all functions and all points within their domain. This expansive definition unlocks the ability to define derivatives and integrals for any function, regardless of its complexity. As a result, generalized limits provide a powerful framework for understanding and manipulating mathematical functions in a more comprehensive way.

The book investigates the applications of generalized limits across various mathematical disciplines, applicable to functional analysis, operator theory, and measure theory. It also explores the intriguing connection between generalized limits and complex mathematical spaces.

Furthermore, the book discusses the potential of generalized limits in physics, particularly in quantum mechanics. By offering novel perspectives for describing elusive physical phenomena, generalized limits contribute to ongoing discussions about the fundamental nature of reality.

Discontinuous Analysis is not just a technical reference but also an invitation to explore the frontiers of mathematics. By bridging the gap between traditional and generalized mathematical concepts, the book fosters a deeper appreciation for the evolution of mathematical thought and its impact on various fields.

The concluding chapters inspire readers to envision the uncharted territories and potential applications that may emerge from the continued exploration of generalized limits.