| 1. | Convergence in probability is also called weak convergence of random variables.
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| 2. | The definition of weak convergence can be extended to Banach spaces.
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| 3. | As the names indicate, weak convergence is weaker than strong convergence.
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| 4. | If a function is weak convergence is usually of interest.
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| 5. | Convergence in total variation is stronger than weak convergence.
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| 6. | Weak convergence is also called "'convergence in distribution " '.
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| 7. | This is the weak convergence of laws without laws being defined except asymptotically.
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| 8. | In fact, strong convergence implies convergence in probability, and convergence in probability implies weak convergence.
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| 9. | The modern theory still carries the imprint . . . [ This concerns weak convergence in arrays ].
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| 10. | This definition of weak convergence can be extended for " S " any metrizable topological space.
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