Is unemployment benefit part of national income measurement? Since unemployment benefit is a form of government spending, which is a component of aggregate expenditure, then shouldn't unemployment benefits be part of national income measurement?
It is included. It is a transfer payment, so the trick is to ensure that the income flow is only counted one time in the national accounting.

Statistics Canada, National Gross Domestic Product by Income and by Expenditure Accounts link to description


  The Income and Expenditure Accounts record the distribution and use of
  income by the six main institutional sectors: households, non-profit
  institutions serving households, general governments, non-financial
  corporations, financial corporations and non-residents. These accounts
  articulate revenues to the sector (including current transfers from
  other sectors, such as employment insurance received) and current
  expenditures of the sector (including transfers to other sectors, such
  as income taxes paid to government).


("Employment insurance" is the Canadian equivalent of unemployment insurance.)