Abstract: 
We study a stochastic control/stopping problem with a series of inequalitytype and equalitytype expectation
constraints in a general nonMarkovian framework. We demonstrate that the stochastic control/stopping problem
with expectation constraints (CSEC) is independent of a specific probability setting and is equivalent to the
constrained stochastic control/stopping problem in weak formulation (an optimization over joint laws of Brownian
motion, state dynamics, diffusion controls and stopping rules on an enlarged canonical space). Using a martingale
problem formulation of controlled SDEs, we characterize the probability classes in weak formulation
by countably many actions of canonical processes, and thus obtain the upper semianalyticity of the CSEC value
function. Then we employ a measurable selection argument to establish a dynamic programming principle (DPP)
in weak formulation for the CSEC value function, in which the conditional expected costs act as additional states
for constraint levels at the intermediate horizon. 
