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As the eukaryotic cell cycle is a complex process, eukaryotes have evolved a network of regulatory proteins, known as the cell cycle control system, which monitors and dictates the progression of the cell through the cell cycle. [5]
The eukaryotic cell cycle consists of four distinct phases: G 1 phase, S phase (synthesis), G 2 phase (collectively known as interphase) and M phase (mitosis and cytokinesis). M phase is itself composed of two tightly coupled processes: mitosis, in which the cell's nucleus divides, and cytokinesis, in which the cell's cytoplasm and cell membrane divides forming two daughter cells.
Continuous functions, monotone functions, step functions, semicontinuous functions, Riemann-integrable functions, and functions of bounded variation are all Lebesgue measurable. [2] A function f : X → C {\displaystyle f:X\to \mathbb {C} } is measurable if and only if the real and imaginary parts are measurable.
Various cell cycle checkpoints are present throughout the course of the cell cycle that determine whether a cell will progress through division entirely. Importantly in replication the G 1 , or restriction, checkpoint makes the determination of whether or not initiation of replication will begin or whether the cell will be placed in a resting ...
The integral of a non-negative general measurable function is then defined as an appropriate supremum of approximations by simple functions, and the integral of a (not necessarily positive) measurable function is the difference of two integrals of non-negative measurable functions. [1]
In measure theory, an area of mathematics, Egorov's theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of measurable functions.It is also named Severini–Egoroff theorem or Severini–Egorov theorem, after Carlo Severini, an Italian mathematician, and Dmitri Egorov, a Russian mathematician and geometer, who published independent proofs respectively ...
Three types of cell division: binary fission (taking place in prokaryotes), mitosis and meiosis (taking place in eukaryotes).. When cells are ready to divide, because cell size is big enough or because they receive the appropriate stimulus, [20] they activate the mechanism to enter into the cell cycle, and they duplicate most organelles during S (synthesis) phase, including their centrosome.
Let (,,) be a measure space, i.e. : [,] is a set function such that () = and is countably-additive. All functions considered in the sequel will be functions :, where = or .We adopt the following definitions according to Bogachev's terminology.