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Legislative Assembly is the name given in some countries to either a legislature, or to one of its branch. The name is used by a number of member-states of the Commonwealth of Nations, as well as a number of other countries.
Legislative Assemblies in the Commonwealth 
The modern-day Legislative Assembly in a Commonwealth country, either as a national or sub-national parliament, is in most cases an evolution of one of these colonial legislative chambers.
In a number of territories, the name House of Assembly is used instead.
Members of Commonwealth Legislative Assemblies 
Members of a Legislative Assembly in a Commonwealth country are usually referred to as a "Member of the Legislative Assembly", commonly abbreviated as MLA; however, in Canada, members of the province of Ontario's Legislative Assembly are known as a "Member of the Provincial Parliament" (MPP, Ontario).
Examples of Legislative Assemblies in Commonwealth countries 
In India, the lower or sole house of each constituent state's parliament is called the Legislative Assembly, or Vidhan Sabha. The same name is also used for the lower house of the legislatures for two of the union territories, Delhi and Puducherry. The upper house in the seven states with a bicameral legislature is called the Legislative Council, or Vidhan Parishad. Members of the former are called MLAs, and those of the latter MLCs.
The lower houses of the parliaments of the Australian states of New South Wales, Victoria and Western Australia are called the Legislative Assembly. In contrast, the state of Queensland has abolished the former upper house of its parliament, leaving the Legislative Assembly as the sole chamber. The sole house of parliament in the Australian Capital Territory is the Legislative Assembly.
In Malaysia, the State Legislative Assemblies of each individual states are known as Dewan Undangan Negeri. There are thirteen State Legislative Assemblies in Malaysia and it is a unicameral legislature.