Lattice Theory: Minkowski's Theorems

Related lectures (31)

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Explores Minkowski's theorems on lattices, volumes, and set comparisons.

Introduces measurable sets, functions, and the Cantor set properties, including ternary development of numbers.

Explores the construction of the Lebesgue function on the Cantor set and its unique properties.

Covers dynamical systems on homogeneous spaces and their interactions with number theory.

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

Covers the concept of outer measure and properties of measurable sets.

Covers the properties of the Lebesgue measure and its existence.

Explores the construction of measures, emphasizing positive functionals and their connection to the Riesz-Kakutani Theorem.

Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.

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