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Related lectures (31)

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Lebesgue Integral: Definition and Properties

Explores the Lebesgue integral, where functions self-select partitions, leading to measurable sets and non-measurable complexities.

Lebesgue Measure: Definition and Properties

Explores the Lebesgue outer measure, its properties, and applications in measure theory.

Hausdorff Dimension and Brownian Motion

Explores the Hausdorff dimension of Brownian motion zeros, demonstrating a dimension of 1/2 with certainty.

Fubini Theorem on Closed Rectangles

Explores the Fubini theorem on closed rectangles in R², discussing integrability, iterated integrals, and compact sets.

Graph Sketching: Connected Components

Covers the concept of graph sketching with a focus on connected components.

Lebesgue Measure and Fourier Analysis

Explores Lebesgue measure, Fourier analysis, PDE applications, and optimal transport in PDEs.

Advanced analysis II

Covers Jordan-measurable sets, Riemann-integrability, and function continuity on compact sets.

Computing leading eigenvalues of the transfer operator

Explores computing the leading eigenvalue of a transfer operator beyond periodic points, focusing on mathematical settings, spectral radius estimation, and the Zaremba Conjecture.

Nonlinear Dynamics: Chaos and Complex Systems

Explores countable and uncountable sets, Cantor set, Mandelbrot set, and Box dimension in nonlinear dynamics and complex systems.

Riemann Integral: Properties and Characterization

Explores the properties and characterization of the Riemann integral on different sets and measurable sets.